what is the potential at point b, which is 4.5 cm to the right of a?
Mastering Physics Solutions Affiliate twenty Electric Potential and Electrical Potential Energy
Mastering Physics Solutions
Chapter 20 Electric Potential and Electrical Potential Energy Q.1CQ
In i region of infinite the electric potential has a positive abiding value. In another region of infinite the potential has a negative constant value. What can be said near the electric field within each of these two regions of space?
Solution:
Chapter xx Electric Potential and Electrical Potential Free energy Q.1P
CE An electron is released from balance in a region of space with nonzero electrical field. Equally the electron moves, does it feel an increasing or decreasing electric potential? Explicate.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.2CQ
2 like charges a distance r apart have a positive electrical potential energy. Conversely, two dissimilar charges a distance r apart take a negative electric potential free energy. Explain the concrete significance of these observations.
Solution:
Electrical potential free energy is the free energy required to carry a charge from a betoken towards some other charge. If they are similar charges so they repel to each other while if they are different charges then an bonny force acts betwixt them past which they are attracted by each other.
If the charges are like and then due to repulsive forcefulness betwixt them an external energy is needed to carry the charge towards another charge, then potential energy is positive. Thus positive potential free energy ways requirement of external energy to carry one charge towards other.
On the other manus, for different charges the electric potential energy is negative which represents that there is no need of external energy to behave 1 charge towards other, ane charge is attracted past attractive force, which acts between them.
Affiliate 20 Electrical Potential and Electrical Potential Energy Q.2P
A compatible electric field of magnitude 4.ane × 105 Northward/C points in the positive x management. Find the alter in electric potential energy of a 4.5-μC charge as information technology moves from the origin to the points (a) (0, vi.0 chiliad); (b) (6.0 m, 0); and (c) (6.0 chiliad, 6.0 chiliad).
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.3CQ
If the electric field is zero in some region of space is the electric potential aught there every bit well? Explain.
Solution:
No, it need not necessary:
The electric field is a mensurate of alter in position. So the electric field is nada in 2 cases.
I) When the electric potential is constant or
II) When the electric potential is zero.
Then the electric potential need not necessarily exist nada. If the electric field is zero. It may be positive or negative.
Chapter twenty Electric Potential and Electric Potential Free energy Q.3P
A uniform electrical field of magnitude six.8 × 105 North/C points in the positive x direction. Notice the modify in electrical potential between the origin and the points (a) (0, six.0 m); (b) (6.0 g, 0); and (c) (6.0 m, vi.0 m).
Solution:
Chapter twenty Electric Potential and Electrical Potential Free energy Q.4CQ
Solution:
Chapter 20 Electrical Potential and Electrical Potential Energy Q.4P
BIO Electrical Potential Across a Cell Membrane In a typical living prison cell, the electric potential within the cell is 0.070 V lower than the electrical potential outside the cell. The thickness of the cell membrane is 0.10 μm. What are the magnitude and management of the electric field within the cell membrane?
Solution:
Chapter xx Electric Potential and Electrical Potential Free energy Q.5CQ
How much work is required to move a charge from one location on an equipotential to another point on the same equipo tential?Explicate.
Solution:
Since the potential difference in the equipotential surface is goose egg, i.due east. ΔV = 0
And then, the work washed for a moving charge in that surface W = q. ΔV
= q.0
= 0
Chapter xx Electric Potential and Electrical Potential Energy Q.5P
A computer monitor accelerates electrons and directs them to the screen in lodge to create an epitome. If the accelerating plates are 1.05 cm apart, and have a potential difference of 25,500 5, what is the magnitude of the compatible electrical field betwixt them?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.6CQ
It is known that the electric potential is abiding on a given two- dimensional surface. What can exist said about the electric field on this surface?
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.6P
Find the change in electric potential energy for an electron that moves from ane accelerating plate to the other in the computer monitor described in the previous problem.
Solution:
Chapter 20 Electrical Potential and Electric Potential Energy Q.7CQ
Explain why equipotenrials are always perpendicular to the electric field.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.7P
A parallel-plate capacitor has plates separated past 0.75 mm. If the electrical field between the plates has a magnitude of (a) one.2 × 105 V/m or (b) 2.4 × 104N/C, what is the potential difference betwixt the plates?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.8CQ
Two charges are at locations that have the same value of the electric potential. Is the electric potential energy the same for these charges? Explain.
Solution:
Chapter twenty Electric Potential and Electrical Potential Free energy Q.8P
When an ion accelerates through a potential difference of 2140 V, its electric potential energy decreases past 1.37 × x-15 J. What is the charge on the ion?
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.9CQ
A capacitor is connected to a battery and fully charged. What becomes of the accuse on the capacitor when information technology is disconnected from the battery? What becomes of the accuse when the two terminals of the capacitor are continued to one another?
Solution:
The charge on the capacitor will remains same even after it is disconnected from the circuit.
When two terminals of the capacitor are continued to one another, the charge flow from plate to plate till the charge on both the plates becomes nil.
Chapter twenty Electric Potential and Electrical Potential Energy Q.9P
The Electric Potential of the Earth The Globe has a vertical electrical field with a magnitude of approximately 100 V/one thousand near its surface. What is the magnitude of the potential departure betwixt a point on the ground and a betoken on the same level as the top of the Washington Monument (555 ft loftier)?
Solution:
Chapter 20 Electrical Potential and Electrical Potential Free energy Q.10CQ
It would exist unwise to unplug a television receiver gear up, take off the back, and reach inside. The reason for the danger is that if yous happen to touch the terminals of a high-voltage capacitor you could receive a large electrical stupor—fifty-fifty though the prepare is unplugged. Why?
Solution:
Even after the goggle box is unplugged, the charge in the high voltage capacitor will remain at that place. So, when you lot come in contact with this capacitor y'all will receive a large electric shock.
Chapter 20 Electrical Potential and Electrical Potential Energy Q.10P
A uni class electrical field with a magnitude of 6350 N/C points in the positive 10 direction. Detect the modify in electric potential energy when a +12.five-μC charge is moved 5.fifty cm in (a) the positive x direction, (b) the negative x direction, and (c) the positive y direction.
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.11CQ
On which of the following quantities does the capacitance of a capacitor depend: (a) the charge on the plates; (b) the separation of the plates; (c) the voltage difference between the plates; (d) the electric field between the plates; or (e) the area of the plates?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.11P
IP A spark plug in a car has electrodes separated by a gap of 0.025 in. To create a spark and ignite the air-fuel mixture in the engine, an electric field of three.0 × 106 V/m is required in the gap. (a) What potential difference must be applied to the spark plug to initiate a spark? (b) If the separation between electrodes is increased, docs the required potential difference increase, decrease, or stay the same? Explain, (c) Find the potential difference for a separation of 0.050 in.
Solution:
Affiliate xx Electric Potential and Electric Potential Energy Q.12CQ
Nosotros say that a capacitor stores accuse, yet the total charge in a capacitor is zero; that is, Q + (−Q) = 0. In what sense does a capacitor store charge if the net charge within it is zilch?
Solution:
Though the net accuse of a capacitor is nothing, charge of opposite signs is stored in 2 different locations. So we can say that a capacitor stores reverse charges separately and even has the energy needed to cause the separation.
Chapter 20 Electric Potential and Electrical Potential Energy Q.12P
Solution:
Affiliate twenty Electric Potential and Electrical Potential Energy Q.13CQ
The plates of a particular parallel-plate capacitor are uncharged. Is the capacitance of this capacitor zero? Explain.
Solution:
No.
The capacitance of this capacitor is non aught even if the plates of the parallel-plate capacitor are uncharged because the term CAPACITANCE defines the chapters of the capacitor which will not be nil.
Chapter 20 Electric Potential and Electrical Potential Energy Q.13P
A Charged Battery A typical 12-5 machine battery can deliver 7.5 × 105 C of charge. If the energy supplied by the battery could be converted entirely to kinetic energy, what speed would it give to a 1400-kg car that is initially at residue?
Solution:
Chapter 20 Electric Potential and Electrical Potential Free energy Q.14P
IP BIO The Sodium Pump Living cells actively "pump" positive sodium ions (Na+) from inside the prison cell to outside the cell. This process is referred to as pumping because work must be done on the ions to move them from the negatively charged inner surface of the membrane to the positively charged outer surface. Given that the electric potential is 0.070 5 higher outside the jail cell than within the cell, and that the jail cell membrane is 0.10 μm thick, (a) summate the work that must be done (in joules) to move i sodium ion from inside the cell to exterior. (b) If the thickness of the cell membrane is increased, does your respond to part (a) increase, decrease, or stay the aforementioned? Explain. (Information technology is estimated that as much as 20% of the energy we consume in a resting state is used in operating this "sodium pump.")
Solution:
Chapter 20 Electrical Potential and Electrical Potential Energy Q.15P
Solution:
Chapter xx Electric Potential and Electrical Potential Energy Q.16P
Points A and B have electric potentials of 332 V and 149 V, respectively. When an electron released from rest at point A arrives at point C, its kinetic energy is KA. When the electron is released from balance at point B, however, its kinetic free energy when it reaches point C is KB = 2KA. What are (a) the electric potential at bespeak C and (b) the kinetic free energy KA?
Solution:
Chapter 20 Electrical Potential and Electric Potential Energy Q.17P
CE Predict/Explain An electron is released from remainder in a region of space with a nonzero electrical field, (a) Every bit the electron
moves, does the electrical potential free energy of the organization increase, decrease, or stay the same? (b) Cull the all-time explanation from amongst the following:
I. Because the electron has a negative charge its electrical potential energy doesn't decrease, as one might expect, only increases instead.
II. Every bit the electron begins to move, its kinetic energy increases. The increase in kinetic energy is equal to the subtract in the electric potential free energy of the organisation.
III. The electron will move perpendicular to the electric field, and hence its electric potential energy will remain the aforementioned.
Solution:
(a) The electron potential free energy decrease This decrease in potential energy converted into the kinetic energy gained by the electron. This is due to the conservation of energy.
(b) So increment in kinetic energy of electron is equal to the decrease in potential free energy of system. So all-time explanation is (Two)
Chapter 20 Electrical Potential and Electrical Potential Energy Q.18P
Calculate the speed of (a) a proton and (b) an electron afterwards each particle accelerates from residue through a potential divergence of 275 V.
Solution:
Chapter twenty Electric Potential and Electric Potential Free energy Q.19P
The electrons in a Telly film tube are accelerated from residue through a potential difference of 25 kV. What is the speed of the electrons after they take been accelerated by this potential difference?
Solution:
Chapter 20 Electrical Potential and Electrical Potential Energy Q.20P
Find the potential difference required to accelerate protons from rest to 10% of the speed of light. (At this point, relativistic effects start to get meaning.)
Solution:
Chapter 20 Electrical Potential and Electric Potential Energy Q.21P
IP A particle with a mass of 3.8 grand and a charge of +0.045 μC is released from residue at indicate A in Figure 20-20. (a) In which direction will this accuse move? (b) What speed volition information technology accept afterwards moving through a distance of v.0 cm? The electric field has a magnitude of 1200 Due north/C. (c) Suppose the particle continues moving for another 5.0 cm. Will its increase in speed for the second v.0 cm be greater than, less than, or equal to its increase in speed in the start 5.0 cm? Explain.
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.22P
A proton has an initial speed of four.0 × 105 yard/s. (a) What potential divergence is required to bring the proton to rest? (b) What potential difference is required to reduce the initial speed of the proton past a factor of 2? (c) What potential deviation is required to reduce the initial kinetic energy of the proton past a gene of two?
Solution:
Chapter twenty Electric Potential and Electrical Potential Free energy Q.23P
Solution:
Chapter 20 Electric Potential and Electrical Potential Free energy Q.24P
CE The accuse q1 in Effigy xx-22 has the value +Q. (a) What value must q2 have if the electrical potential at point B is to be zero? (b) With the value for q2 found in part (a), is the electric potential at point A positive, negative, or null? Explain.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.25P
CE It is given that the electric potential is naught at the center of the square in Figure 20-22. (a) If q1 = +Q, what is the value of the charge q2? (b) Is the electrical potential at signal A positive, negative, or nothing? Explain, (c) Is the electrical potential at point B positive, negative, or zippo? Explicate.
Solution:
The to a higher place value shows the net electric potential at point B is negative. This is because the point B is closer to the negative accuse as compare to positive charge. The electric potential is inversely proportional to distance of the point from the charge. The less distance from the negative charge implies that the potential due to negative charge is greater than the potential due to positive accuse.
Hence, the cyberspace electrical potential at point B is .negative
Chapter twenty Electric Potential and Electrical Potential Energy Q.26P
The electric potential i.1 thou from a bespeak charge q is two.8 × 104 V. What is the value of q?
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.27P
A point charge of -7.2 μC is at the origin. What is the electric- potential at (a) (3.0 m, 0); (b) (−three.0 one thousand, 0); and (c) (iii.0 m,-three.0 m)
Solution:
Chapter 20 Electrical Potential and Electrical Potential Free energy Q.28P
The Bohr Atom The hydrogen atom consists of one electron and one proton, hi the Bohr model of the hydrogen cantlet the electron orbits the proton in a circular orbit of radius 0.529 × 10-10 m. What is the electric potential due to the proton at the electron'due south orbit?
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.29P
How far must the point charges q1 = +vii.22 μC and q2 = −26.one μC be separated for the electric potential energy of the system to be −126 J?
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.30P
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.31P
IP Betoken charges +4.1 μC and −2.2μC are placed on the 10 axis at (11 grand, 0) and (−11 m, 0), respectively, (a) Sketch the electric potential on the ten axis for this system, (b) Your sketch should show one point on the x centrality between the two charges where the potential vanishes. Is this betoken closer to the +4.i-−μC accuse or closer to the −ii.two-μC charge? Explicate, (c) Discover the betoken referred to in part (b).
Solution:
Chapter xx Electric Potential and Electrical Potential Energy Q.32P
IP (a) In the previous trouble, observe the point to the left of the negative charge where the electric potential vanishes, (b) Is the electric field at the signal institute in role (a) positive, negative, or zippo? Explain.
Solution:
Affiliate 20 Electric Potential and Electrical Potential Free energy Q.33P
A dipole is formed by signal charges +3.half-dozen μC and −3.6 μC placed on the x axis at (0.25 m, 0) and (-0.25 m, 0), respectively. (a) Sketch the electric potential on the x axis for this arrangement. (b) At what positions on the ten centrality does the potential take the value 7.v × 105 5?
Solution:
Chapter 20 Electric Potential and Electric Potential Energy Q.34P
A charge of 3.05 μC is held fixed at the origin. A second charge of three.05 μC is released from residual at the position (1.25 g, 0.570 m). (a) Tf the mass of the 2nd charge is ii.16 thousand, what is its speed when it moves infinitely far from the origin? (b) At what distance from the origin does the second charge accomplish half the speed it volition take at infinity?
Solution:
Therefore the 2d particle attains half of the speed at infinity at a distance of 1.84m from the origin.
Affiliate 20 Electric Potential and Electrical Potential Energy Q.35P
Solution:
Chapter 20 Electric Potential and Electric Potential Energy Q.36P
A charge of -2.205 μC is located at (3.055 grand, four.501 in), and a charge of 1.800 μC is located at (−2.533 one thousand, 0). (a) Find the electric potential at tine origin, (b) In that location is one point on the line connecting these two charges where the potential is zip. Find this point.
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.37P
Solution:
Chapter 20 Electrical Potential and Electrical Potential Energy Q.38P
How much work must exist done to move the three charges in Figure 20-24 infinitely far from 1 another?
Solution:
Chapter 20 Electric Potential and Electric Potential Free energy Q.39P
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.40P
A square of side a has a accuse +Q at each corner. What is the electric potential energy of this system of charges?
Solution:
Chapter xx Electrical Potential and Electrical Potential Free energy Q.41P
Solution:
Chapter twenty Electric Potential and Electric Potential Energy Q.42P
CE Predict/Explicate A positive charge is moved from one location on an equipotential to some other point on the same equipotential. (a) Is the work done on the charge positive, negative, or naught? (b) Choose the best explanation from amidst the post-obit: I. The electrical field is perpendicular to an equipotential, therefore the piece of work done in moving along an equipotential is nil.
I. Considering the charge is positive the work done on it is also positive.
II. It takes negative piece of work to keep the positive accuse from accelerating every bit it moves along the equipotential.
Solution:
(a) Given,
A positive charge is moved from i location to some other location in which both the locations are at same equipotential. Since the positive charge is moving in same equipotential at that place is no work done by the positive charge considering of same equipotential. So piece of work done in moving the positive accuse from i identify to some other place is zero.
(b) The electric field is perpendicular to an equipotential therefore the piece of work washed in moving along equipotential is zero.
Therefore is the all-time caption.
Chapter 20 Electric Potential and Electric Potential Energy Q.43P
CE Predict/Explain (a) Is the electrical potential at betoken 1 in Figure xx-19 greater than, less than, or equal to the electrical potential at indicate three? (b) Choose the all-time explanation from amid the following:
I. The electric field lines bespeak to the correct, indicating that the electric potential is greater at betoken 3 than at point 1.
II. The value of the electric potential is large where the electric field lines are close together, and minor where they are widely spaced. Therefore, the electric potential is the aforementioned at points 1 and 3.
Iii· The electric potential decreases every bit nosotros move in the direction of the electric field, equally shown in Figure xx-3. Therefore, the electric potential is greater at betoken one than at point 3.
Solution:
(a) The electric potential at point 1 is greater than the electric potential at point iii.
(b) We know that the management of electric field is from high potential to low potential. Therefore the electric potential volition decrease when we motility in the field direction. In the figure the management of electrical field is from signal 1 to bespeak 3. And then the electric potential at signal 1 is greater than the electric potential at betoken 3.
Therefore option III is the best caption.
Chapter 20 Electric Potential and Electrical Potential Energy Q.44P
CE Predict/Explain Imagine sketching a big number of equipotential surfaces in Figure 20-19, with a constant difference in electric potential between adjacent surfaces, (a) Would the equipotentials at indicate 2 be more closely spaced, be less closely spaced, or accept the same spacing every bit equipotentials at point i? (b) Choose the best caption from among the post-obit:
I. When electrical field lines are close together, the corresponding equipotentials are far apart.
Two. Equipotential surfaces, by definition, e'er take equal spacing between them.
3. The electric field is more intense at point 2 than at betoken 1, which means the equipotential surfaces are more closely spaced in that region.
Solution:
(a) When nosotros describe large number of equipotential surfaces with abiding potential difference between side by side surfaces, the equipotentials at point 2 are more closely spaced equally equipotentials at point1.
Annotate
(b) From the figure it is clear that the electric field is more than intense most indicate ii than well-nigh betoken i, considering the field lines are packed more closely together near betoken 2. This means, in plow, that the electrical potential changes more rapidly with position at point two. As a result, the spacing between equipotential surfaces at point 2 is less than the spacing between equipotential surfaces at point 1.
Therefore choice Iii is the best caption.
Chapter xx Electric Potential and Electric Potential Energy Q.45P
Ii indicate charges are on the x axis. Charge ane is +q and is located at x = −1.0 m; charge 2 is −2q and is located at x = 1.0 k. Brand sketches of the equipotential surfaces for this system (a) out to a distance of well-nigh 2.0 m from the origin and (b) far from the origin, In each example, indicate the management in· which the potential increases.
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.46P
2 bespeak charges are on the 10 axis. Charge i is +q and is located at x = −i.0 m; charge 2 is +2q and is located at x − 1.0 m. Brand sketches of the equipotential surfaces for this system (a) out to a distance of about 2.0 m from the origin and (b) far from the origin. In each instance, bespeak the direction in which the potential increases.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.47P
Solution:
Chapter twenty Electric Potential and Electric Potential Energy Q.48P
IP Consider a region in space where a uniform electric field E = 6500 N/C points in the negative x direction, (a) What is the orientation of the equipotential surfaces? Explain, (b) If you
movement in the positive ten management, does the clectric potential increase or subtract? Explain, (c) What is the distance between the +xiv-Five and the +16-Five equipotentials?
Solution:
Chapter 20 Electrical Potential and Electrical Potential Energy Q.49P
Solution:
Chapter 20 Electrical Potential and Electrical Potential Energy Q.50P
A 0.40−μF capacitor is connected to a ix.0-5 battery. How much accuse is on each plate of the capacitor?
Solution:
Affiliate 20 Electric Potential and Electrical Potential Free energy Q.51P
Information technology is desired that 5.viii μC of charge be stored on each plate of a 3.2-μ F capacitor. What potential departure is required between the plates?
Solution:
Chapter 20 Electric Potential and Electric Potential Energy Q.52P
To operate a given flash lamp requires a charge of 32 μC. What capacitance is needed to store this much charge in a capacitor with a potential difference between its plates of ix.0 V?
Solution:
Chapter 20 Electrical Potential and Electric Potential Energy Q.53P
A parallel-plate capacitor is made from two aluminum-foil sheets, each 6.three cm broad and five.four thousand long. Between the sheets is a Teflon strip of the same width and length that is 0.035 mm thick. What is the capacitance of this capacitor? (The dielectric abiding of Teflon is ii.1.)
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.54P
parallel-plate capacitor is synthetic with circular plates of radius 0.056 m. The plates are separated by 0.25 mm, and the space between the plates is filled with a dielectric with dielectric constant κ. When the charge on the capacitor is 1.2 μC the potential difference between the plates is 750 V. Find the value of the dielectric constant, κ.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.55P
IP A parallel-plate capacitor has plates with an surface area of 0.012 m2 and a separation of 0.88 mm. The space between the plates is filled with a dielectric whose dielectric constant is 2.0. (a) What is the potential difference betwixt the plates when the accuse on the capacitor plates is 4.7 μC? (b) Volition your answer to part (a) increment, decrease, or stay the same if the dielectric constant is increased? Explain, (c) Calculate the potential divergence for the case where the dielectric constant is 4.0.
Solution:
Chapter twenty Electrical Potential and Electrical Potential Energy Q.56P
IP Consider a parallel-plate capacitor constructed from two circular metal plates of radius R. The plates arc separated by a altitude of one.v mm. (a) What radius must the plates have if the capacitance of this capacitor is to be ane.0 μF? (b) If the separation between the plates is increased, should the radius of the plates be increased or decreased to maintain a capacitance of 1.0 μF? Explicate, (c) Find the radius of the plates that gives a capacitance of 1.0 μF for a plate separation of 3.0 mm.
Solution:
Chapter 20 Electric Potential and Electrical Potential Free energy Q.57P
A parallel-plate capacitor has plates of area three.45 × 10-4 m2. What plate separation is required if the capacitance is to be 1630 pF? Assume that the space between the plates is filled with (a) air or (b) paper.
Solution:
Chapter 20 Electrical Potential and Electrical Potential Energy Q.58P
IP A parallel-plate capacitor filled with air has plates of are 0.0066 m2 and a separation of 0.45 mm. (a) Detect the magnitude of the accuse on each plate when the capacitor is connected to a 12-V battery, (b) Will your answer to part (a) increase, decrease or stay the same if the separation betwixt the plates is increased? Explain, (c) Summate the magnitude of the charge on the plates if the separation is 0.xc mm.
Solution:
Chapter xx Electric Potential and Electric Potential Free energy Q.59P
Suppose that after walking across a carpeted floor you reach for a doorknob and just earlier you touch it a spark jumps 0.50 cm from your finger to the knob. Discover the minimum voltage needed between your finger and the doorknob to generate this spark.
Solution:
Chapter twenty Electrical Potential and Electrical Potential Energy Q.60P
(a) What plate surface area is required if an air-filled, parallel-plate capacitor with a plate separation of two.6 mm is to have a capacitance of 22 pF? (b) What is the maximum voltage that can exist applied to this capacitor without causing dielectric breakup?
Solution:
Affiliate 20 Electrical Potential and Electric Potential Energy Q.61P
Lightning Every bit a crude model for lightning, consider the ground to be one plate of a parallel-plate capacitor and a deject at an altitude of 550 thou to be the other plate. Presume the surface surface area of the deject to exist the same equally the area of a square that is 0.50 km on a side, (a) What is the capacitance of this capacitor? (b) How much charge can the cloud hold before the dielectric strength of the air is exceeded and a spark (lightning) results?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.62P
A parallel-plate capacitor is made from 2 aluminum-foil sheets, each iii.00 cm wide and ten.0 m long. Between the sheets is a mica strip of the same width and length that is 0.0225 mm thick. What is the maximum charge that tin can be stored in this capacitor? (The dielectric abiding of mica is 5.iv, and its dielectric strength is 1.00 x 108V/thousand.)
Solution:
Chapter 20 Electric Potential and Electric Potential Free energy Q.63P
Calculate the work done by a three.0-V battery as it charges a 7.8-μF capacitor in the flash unit of measurement of a camera
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.64P
BIO Defibrillator An automatic external defibrillator (AED) delivers 125 J of energy at a voltage of 1050 Five. What is the capacitance of this device?
Solution:
Chapter 20 Electrical Potential and Electrical Potential Energy Q.65P
IP BIO Cell Membranes The membrane of a living prison cell can be approximated past a parallel-plate capacitor with plates of area 4.75 × 10-9 m2, a plate separation of 8.5 × 10-9 m, and a dielectric with a dielectric constant of four.5. (a) What is the energy stored in such a cell membrane if the potential difference across it is 0.0725 5? (b) Would your respond to function (a) increase, decrease, or stay the same if the thickness of the jail cell membrane is increased? Explain.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.66P
A 0.22-μF capacitor is charged by a ane.5-Five bombardment. After being charged, the capacitor is connected to a minor electrical motor. Assuming 100% efficiency, (a) to what summit can the motor lift a 5.0-g mass? (b) What initial voltage must the capacitor have if it is to elevator a 5.0-chiliad mass through a height of 1.0 cm?
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.67P
Discover the electric free energy density between the plates of a 225-μF parallel-plate capacitor. The potential difference between the plates is 345 5, and the plate separation is 0.223 mm.
Solution:
Chapter xx Electric Potential and Electrical Potential Energy Q.68P
What electric field strength would store 17.5 Jof energy in every i.00 mm3 of space?
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.69P
An electronic flash unit for a camera contains a capacitor with a capacitance of 890 μF. When the unit is fully charged and fix for operation, the potential difference betwixt the capacitor plates is 330 V. (a) What is the magnitude of the charge on each plate of the fully charged capacitor? (b) Detect the energy stored in the "charged-up" wink unit.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.70P
A parallel-plate capacitor has plates with an area of 405 cm2 and an air-filled gap between the plates that is 2.25 mm thick. The capacitor is charged by a battery to 575 V and and then is dis- connected from the battery, (a) How much energy is stored in the capacitor? (b) The separation between the plates is now in- creased to 4.l mm. How much energy is stored in the capacitor at present? (c) How much work is required to increase the separation of the plates from ii.25 mm to four.50 mm? Explain your reasoning.
Solution:
Chapter xx Electric Potential and Electrical Potential Energy Q.71GP
CE A proton is released from rest in a region of infinite with a nonzero electric field. As the proton moves, does information technology feel an increasing or decreasing electrical potential? Explain.
Solution:
Apply the concept of electric field and the direction of electric field lines to discuss the motion of a charged particle in not-zero electric field.
In electrostatics, the positively charged region is treated every bit higher potential region and the negatively charged region is treated every bit lower potential region. The electric fields lines e'er points from the higher potential region to the lower potential region. Since the proton is a positively charged particle, the proton movement is in the line of direction of the electrical field that is information technology travels towards the lower potential region. Therefore, the proton travels experience decreasing electrical potential in the not-zero electric field region.
Affiliate 20 Electrical Potential and Electrical Potential Energy Q.72GP
CE Predict/Explain A proton is released from rest in a region of space with a nonzero electrical field, (a) As the proton moves, does the electric potential energy of the arrangement increase, decrease, or stay the aforementioned? (b) Cull the best explanation from among the following:
I. As the proton begins to motion, its kinetic energy increases. The increase in kinetic energy is equal to the decrease in the electric potential energy of the system.
2. Considering the proton has a positive charge, its electric potential free energy will always increase.
Three. The proton will move perpendicular to the electrical field, and hence its electric potential energy will remain the same.
Solution:
(a)
If the proton released from balance in the region of space with not-aught electric field information technology gains kinetic energy.
From the conservation of energy, total free energy (Sum of kinetic free energy and electrical potential free energy) of the arrangement is abiding.
Then the electric potential free energy of the proton must decrease to increase the kinetic energy of the proton.
(b)
As proton begins to move, its kinetic energy increases.
The increases in the kinetic free energy are equal to the decrease in the electric potential energy of the arrangement.
ANS: I
Chapter xx Electric Potential and Electric Potential Energy Q.73GP
CE In the Bohr model of the hydrogen atom, a proton and an electron are separated by a constant distance r. (a) Would the clectric potential free energy of the system increase, decrease, or stay the same if the electron is replaced with a proton? Explain, (b) Suppose, instead, that the proton is replaced with an electron. Would the electrical potential energy of the system increase, decrease, or stay the aforementioned? Explicate.
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.74GP
CE The plates of a parallel-plate capacitor have constant charges of +Q and-Q. Practice the following quantities increase, decrease, or remain the same as the separation of the plates is increased? (a) The electrical field betwixt the plates; (b) the potentiell difference betwixt the plates; (c) the capacitance; (d) the energy stored in the capacitor.
Solution:
Chapter xx Electric Potential and Electrical Potential Energy Q.75GP
CE A parallel-plate capacitor is connected to a bombardment that maintains a abiding potential difference Five between the plates. If the plates of the capacitor are pulled further autonomously, practise the post-obit quantities increase, decrease, or remain the same? (a) The electric field between the plates; (b) the charge on the plates; (c) the capac- itance; (d) the free energy stored in the capacitor.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.76GP
CE The plates of a parallel-plate capacitor have constant charges of +Q and −Q. Practise the following quantities increase, decrease, or remain the same every bit a dielectric is inserted betwixt the plates? (a) The electric field betwixt the plates; (b) the potential divergence between the plates; (c) the capacitance; (d) the energy stored in the capacitor.
Solution:
Chapter twenty Electric Potential and Electric Potential Energy Q.77GP
CE A parallel-plate capacitor is continued to a battery that maintains a constant potential difference Five betwixt the plates. If a dielectric is inserted betwixt the plates of the capacitor, do the following quantities increase, decrease, or remain the same? (a) The electric field betwixt,the plates; (b) the charge on the plates; (c) the capaci tance; (d) the energy stored in the capacitor.
Solution:
Chapter 20 Electric Potential and Electrical Potential Free energy Q.78GP
Notice the difference in electric potential, ΔV = VB — VA between the points A and B for the following cases: (a) The electrical field does 0.052 J of piece of work as you move a +five.7-μC charge from A to B. (b) The electric field does -0.052 J of work as you movement a −5.seven-μC accuse from A to B. (c) Yous perform 0.052 J of work as you slowly move a +5.vii-μC charge from A to B.
Solution:
Chapter 20 Electric Potential and Electric Potential Energy Q.79GP
The separation between the plates of a parallel-plate capacitor is doubled and the area of the plates is halved. How is the capacitance affected?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.80GP
A parallel-plate capacitor is continued to a battery that maintains a abiding potential deviation between the plates. If the spacing between the plates is doubled, how is the magnitude of charge on the plates affected?
Solution:
Chapter xx Electric Potential and Electrical Potential Free energy Q.81GP
CE Two bespeak charges arc placed on the 10 axis. The charge +2q is at x = 1.5 yard, and the charge —q is at ten = −1.5 1000. (a) There is a point on the x axis between the two charges where the electric potential is goose egg. Where is this indicate? (b) The electrical potential too vanishes at a point in one of the following regions: region i, x between 1.5 yard and 5.0 m; region ii, x between −one.5 m and −iii.0 chiliad; region iii, x between −3.5 grand and −5.0 thou. Place the advisable region, (c) Find the value of x referred to in role (b).
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.82GP
A accuse of 24.v μC is located at (iv.40 one thousand, 6.22 yard), and a charge of −eleven.2 μC is located at (−4.50 m, 6.75 m). What accuse must exist located at (two.23 m, −3.31 m) if the electric potential is to be nil at the origin?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.83GP
The Bohr Model In the Bohr model of the hydrogen atom (see Problem 28) what is the smallest corporeality of work that must be done on the electron to move it from its circular orbit, with a radius of 0.529 × 10−10 m, to an infinite distance from the proton? This value is referred to equally the ionization energy of hydrogen.
Solution:
Chapter xx Electric Potential and Electrical Potential Free energy Q.84GP
Solution:
Chapter 20 Electric Potential and Electric Potential Energy Q.85GP
Repeat Trouble 84 for the case where both charges arc +1.2 μC.
Solution:
Chapter 20 Electric Potential and Electrical Potential Free energy Q.86GP
How much work is required to bring 3 protons, initially infinitely far apart, to a configuration where each proton is one.5 × 10-xv m from the other two? (This is a typical separation for protons in a nucleus.) ·
Solution:
Chapter twenty Electric Potential and Electric Potential Free energy Q.87GP
A bespeak charge Q = +87.1 μC is held fixed at the origin. A 2d signal charge, with mass g = 0.0576 kg and charge q = −two.87 μC, is placed at the location (0.323 chiliad, 0). (a) Find the clectric potential energy of this system of charges, (b) If the second charge is released from remainder, what is its speed when it reaches the point (0.121 m, 0)?
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.88GP
Electron Escape Speed An electron is at rest just above the surface of a sphere with a radius of ii.7 mm and a uniformly distributed positive accuse of 1.8 × 10-xv C. Like a rocket diggings off from the Globe, the electron is given an initial speed vc radially
outward from the sphere. If the electron coasts to infinity, where its kinetic energy drops to zero, what is the escape speed, ve?
Solution:
Affiliate xx Electric Potential and Electrical Potential Energy Q.89GP
Quark Model of the Neutron According to the quark model of cardinal particles, neutrons—the neutral particles in an cantlet'southward nucleus—are composed of 3 quarks. Two of these quarks are "downward" quarks, each with a charge of —due east/3; the third quark is an "up" quark, with a charge of +2e/3. This gives the neutron a cyberspace charge of zero. What is the electric potential energy of these three quarks, bold they are equidistant from one another, with a separation distance of 1.three × ten-fifteen grand? (Quarks are discussed in Chapter 32.)
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.90GP
A parallel-plate capacitor is charged to an electrical potential of 325 V by moving 3.75 × 1016 electrons from ane plate to the other. How much work is washed in charging the capacitor?
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.91GP
IP The iii charges shown in Effigy 20-25 are held in identify every bit a fourth charge, q, is brought from infinity to the indicate P. The charge q starts at rest at infinity and is too at rest when it is placed at the indicate P. (a) If q is a positive charge, is the work required to bring it to the bespeak P positive, negative, or zero? Explain. (b) Find the value of (/ if the work needed to bring it to indicate P is −ane.iii × 10-eleven J.
Solution:
Affiliate 20 Electric Potential and Electrical Potential Energy Q.92GP
(a) In Figure xx-28 we see that the electric potential increases by ten.0 V as one moves iv.00 cm in the positive x management. Use this information to calculate the x component of the electrical field. (Ignore the y management for the moment.) (b) Apply the aforementioned reasoning equally in part (a) to calcidate the y component of the electric field, (c) Combine the results from parts (a) and (b) to find the magnitude and direction of the electric field for this system.
Solution:
Chapter xx Electrical Potential and Electrical Potential Energy Q.93GP
IP BIO Electrical Catfish The electric catfish (Malapterurs electricus) is an aggressive fish, i.0 m in length, found today in tropical Africa (and depicted in Egyptian hieroglyphics). The catfish is capable of generating jolts of electricity upwards to 350 5 past producing a positively charged region of muscle near the caput and a negatively charged region virtually the tail, (a) For the same corporeality of accuse, can the catfish generate a college voltage by separating the charge from 1 cease of its body to the other, as it does, or from one side of the body to the other? Explicate, (b) Estimate the charge generated at each end of a catfish as follows: Treat the catfish as a parallel-plate capacitor with plates of area 1.8 × x-two m2, separation ane.0 chiliad, and filled with a dielectric with a dielectric abiding 1000 = 95.
Solution:
Chapter 20 Electrical Potential and Electric Potential Energy Q.94GP
As a +six.2-μC charge moves along the x axis from x = 0 to 10 = 0.70 m, the electric potential it experiences is shown in Figure 20-21. Find the guess location(s) of the charge when its electric potential energy is (a) ii.vi × ten—v J and (b) four.3 × x—5 J.
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.95GP
IP Estimator Keyboards Many estimator keyboards operate on the principle of capacitance. Every bit shown in Figure 20-xvi, each primal forms a small parallel-plate capacitor whose separation is reduced when the primal is depressed, (a) Does depressing a key increase or decrease its capacitance? Explicate, (b) Suppose the plates for each central have an area of 47.5 mm2,and an initial separation of 0.550 mm. In add-on, permit the dielectric have a dielectric constant of three.75. If the circuitry of the computer can detect a change in capacitance of 0.425 pF, what is the minimum distance a primal must be depressed to be detected?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.96GP
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.97GP
BIO Cell Membranes and Dielectrics Many cells in the trunk accept a cell membrane whose inner and outer surfaces acquit opposite charges, just like the plates of a parallel-plate capacitor. Suppose a typical cell membrane has a thickness of 8.1 × ten-9 m, and its inner and outer surfaces conduct accuse densities of −0.58 × 10 3 C/m2 and +0.58 × ten-three C/m2, respectively. In addition, presume that the textile in the cell membrane has a dielectric abiding of v.5. (a) Find the direction and magnitude of the electrical field within the prison cell membrane, (b) Calculate the potential deviation between the inner and outer walls of the membrane, and point which wall of the membrane has the college potential.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.98GP
Long, long ago, on a planet far, far away, a physics experiment was carried out. First, a 0.250-kg ball with naught net charge was dropped from rest at a height of 1.00 1000. The ball landed 0.552 s later. Next, the ball was given a net charge of seven.75 μC and dropped in the aforementioned way from the same height. This time the ball fell for 0.680 s before landing. What is the electrical potential at a top of 1.00 grand to a higher place the basis on this planet, given that the electric potential at ground level is naught? (Air resistance can exist ignored.)
Solution:
Chapter twenty Electric Potential and Electrical Potential Free energy Q.99GP
Rutherford'due south Planetary Model of the Atom In 1911, Ernest Rutherford developed a planetary model of the cantlet, in which a small positively charged nucleus is orbited by electrons. The model was motivated by an experiment carried out by Rutherford and his graduate students, Geiger and Marsden. In can s experiment, they fired alpha particles with an initial speed of 1.75 × 107 grand/due south at a tin can northward canvas of golden. (Blastoff particles are obtained from certain radioactive decays. They take a accuse of +2e and a mass of 6.64 × 10-27 kg.) Flow shut can the alpha particles get to a golden nucleus (accuse = +79e), assuming the nucleus remains stationary? (This calculation sets an upper limit on the size of the golden nucleus. See Chapter 31 for farther details.)
Solution:
The work energy theorem states that the full work done of a organization is equal to its modify in kinetic free energy.
Chapter twenty Electric Potential and Electrical Potential Energy Q.100GP
IP (a) One of the — Q charges in Figure twenty-26 is given an outward "kick" that sends it off with an initial speed V0 wIn le the other three charges are held at remainder. If the moving charge has a mass m, what is its speed when information technology is infinitely far from the other charges? (b) Suppose the remaining — Q charge, wIn ch also has a mass m, is now given the same initial speed, V0. When it is infinitely far away from the ii +Q charges, is its speed greater than, less than, or the same as the speed found in role (a)? Explain.
Solution:
Chapter 20 Electric Potential and Electric Potential Energy Q.101GP
Figure twenty-thirty shows a charge q = +6.77 μC with a mass m = 0.071 kg suspended by a thread of length L = 0.022 one thousand betwixt the plates of a capacitor, (a) Plot the electrical potential free energy of the system every bit a function of the angle θ the thread makes with the vertical. (The electric field between the plates has a magnitude E = 4.16 × 104 V/m.) (b) Repeat function (a) for
tine instance of the gravitational potential energy of the organization, (c) Show that the total potential energy of the system (electric plus gravitational) is a minimum when the angle θ satisfies the equilibrium condition for the charge, tan θ = qE/mg. TIn s relation implies that θ = 22°.
Solution:
Affiliate 20 Electric Potential and Electrical Potential Free energy Q.102GP
The electric potential a distance r from a point charge q is 2.70 × 104 V. One meter further away from the accuse the potential is 6140 V. Find the charge q and the initial distance r.
Solution:
Chapter 20 Electric Potential and Electric Potential Energy Q.103GP
Referring to Problem 84, calculatc and plot the electric potential on the circle centered at (0.50 yard, 0). Give your results in terms of the angle ×, defined every bit follows: θ is the angle measured counterclockwise from a vertex at the eye of the circumvolve, with θ = 0 at bespeak C.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.104GP
When the potential difference between the plates of a capacitor is increased past 3.25 Five, the magnitude of the accuse on each plate increases by 13.five μC. What is the capacitance of this capacitor?
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.105PP
The electrical potential a distance r from a point charge q is 155 V, and the magnitude of the elcctric field is 2240 N/C. Detect the values of q and r.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.106PP
Electrical eels produce an electric field witIn n their body. In which management does the electric field point?
A. toward the head
B. toward the tail
C. upward
D. downward
Solution:
Every bit the muscle cells chosen electro plaques producing each of 0.15V, these electro plaques are producing voltage in the torso of eel together by producing the positive charge at head and negative charge at tail.
And then electric field in the eel body is directed toward the tail.
So the correct option is (B)
Affiliate 20 Electric Potential and Electrical Potential Energy Q.107PP
As a rough approximation, consider an electric eel to be a parallel-plate capacitor with plates of surface area ane.8 × ten-ii m2 separated by 2.0 m and filled with a dielectric whose dielectric abiding is κ = 95. What is the capacitance of the eel in this model?
A. 8.0 × 10-14 F
B. 7.6 × 10-12 F
C. ane.5 ×10-11 F
D. 9.3 ×10-8 F
Solution:
Chapter twenty Electric Potential and Electrical Potential Energy Q.108PP
In terms of the parallel-plate model of the previous problem, how much charge does an electrical eel generate at each end of its body when it produces a voltage of 650 V?
A. 1.2 ×ten-14C
B. v.2 ×10-11 C
C. 4.9×x-ix C
D. 6.ane ×10-5C
Solution:
Affiliate 20 Electric Potential and Electric Potential Energy Q.109PP
How much energy is stored by an electric eel when it is charged up to 650 V. Use the same parallel-plate model discussed in the previous two problems.
A. 1.eight ×10-17J
B. i.seven ×10-8J
C. 1.6×10-6J
D. 2.0×10-2J
Solution:
Chapter 20 Electric Potential and Electric Potential Free energy Q.110PP
IP Referring to Instance 20-3 Suppose the accuse -2q at x = 1.00 yard is replaced with a charge -3q, where q = iv.11 ×ten-nine C. The charge +q is at the origin, (a) Is the electric potential positive, negative, or zip at the point x = 0.333 m? Explain. (b) Find the betoken between x = 0 and ten = 1.00 chiliad where the electric potential vanishes, (c) Is there a bespeak in the region 10 < 0 where the clectric potential passes through nil?
Solution:
Chapter 20 Electrical Potential and Electrical Potential Energy Q.111IP
Referring to Example 20-three Suppose nosotros can alter the location of the charge −2q on the x axis. The charge +q (where q = 4.11 × 10-9C) is still at the origin, (a) Where should the charge −2q be placed to ensure that the electrical potential vanishes at x = 0.500 thousand? (b) With the location of −2q found in function (a), where does the clectric potential pass through zero in the region 10 < 0?
Solution:
Affiliate xx Electric Potential and Electrical Potential Energy Q.112IP
IP Referring to Example xx-3 Suppose the charge +q at the origin is replaced with a charge +5q, where q = 4.11 × x-ix C. The charge -2q is still at x = 1.00 thou. (a) Is there a indicate in the region 10<0 where the electric potential passes through zero? (b) Observe the location between x = 0 and x = i.00 m where the electric potential passes through zero, (c) Detect the location in the region x > 1.00 m where the electric potential passes through cypher.
Solution:
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