Mastering Physics Solutions Chapter 20 Electric Potential and Electrical Potential Energy
Chapter 20 Electric Potential and Electrical Potential Energy Q.1CQ
In one region of space the electric potential has a positive constant value. In another region of space the potential has a negative constant value. What can be said about the electric field within each of these two regions of space?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.1P
CE An electron is released from rest in a region of space with nonzero electric field. As the electron moves, does it experience an increasing or decreasing electric potential? Explain.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.2CQ
Two like charges a distance r apart have a positive electric potential energy. Conversely, two unlike charges a distance r apart have a negative electric potential energy. Explain the physical significance of these observations.
Solution:
Electric potential energy is the energy required to carry a charge from a point towards another charge. If they are like charges then they repel to each other while if they are unlike charges then an attractive force acts between them by which they are attracted by each other.
If the charges are like then due to repulsive force between them an external energy is needed to carry the charge towards another charge, so potential energy is positive. Thus positive potential energy means requirement of external energy to carry one charge towards other.
On the other hand, for unlike charges the electric potential energy is negative which represents that there is no need of external energy to carry one charge towards other, one charge is attracted by attractive force, which acts between them.
Chapter 20 Electric Potential and Electrical Potential Energy Q.2P
A uniform electric field of magnitude 4.1 × 105 N/C points in the positive x direction. Find the change in electric potential energy of a 4.5-μC charge as it moves from the origin to the points (a) (0, 6.0 m); (b) (6.0 m, 0); and (c) (6.0 m, 6.0 m).
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 zero there as well? Explain.
Solution:
No, it need not necessary:
The electric field is a measure of change in position. So the electric field is zero in two cases.
I) When the electric potential is constant or
II) When the electric potential is zero.
So the electric potential need not necessarily be zero. If the electric field is zero. It may be positive or negative.
Chapter 20 Electric Potential and Electrical Potential Energy Q.3P
A uniform electric field of magnitude 6.8 × 105 N/C points in the positive x direction. Find the change in electric potential between the origin and the points (a) (0, 6.0 m); (b) (6.0 m, 0); and (c) (6.0 m, 6.0 m).
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.4CQ
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.4P
BIO Electric Potential Across a Cell Membrane In a typical living cell, the electric potential inside the cell is 0.070 V lower than the electric potential outside the cell. The thickness of the cell membrane is 0.10 μm. What are the magnitude and direction of the electric field within the cell membrane?
Solution:
Chapter 20 Electric Potential and Electrical Potential 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?Explain.
Solution:
Since the potential difference in the equipotential surface is zero, i.e. ΔV = 0
So, the work done for a moving charge in that surface W = q. ΔV
= q.0
= 0
Chapter 20 Electric Potential and Electrical Potential Energy Q.5P
A computer monitor accelerates electrons and directs them to the screen in order to create an image. If the accelerating plates are 1.05 cm apart, and have a potential difference of 25,500 V, what is the magnitude of the uniform electric field between them?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.6CQ
It is known that the electric potential is constant on a given two- dimensional surface. What can be said about the electric field on this surface?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.6P
Find the change in electric potential energy for an electron that moves from one accelerating plate to the other in the computer monitor described in the previous problem.
Solution:
Chapter 20 Electric Potential and Electrical 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 by 0.75 mm. If the electric field between the plates has a magnitude of (a) 1.2 × 105 V/m or (b) 2.4 × 104N/C, what is the potential difference between 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 20 Electric Potential and Electrical Potential Energy Q.8P
When an ion accelerates through a potential difference of 2140 V, its electric potential energy decreases by 1.37 × 10-15 J. What is the charge on the ion?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.9CQ
A capacitor is connected to a battery and fully charged. What becomes of the charge on the capacitor when it is disconnected from the battery? What becomes of the charge when the two terminals of the capacitor are connected 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 connected to one another, the charge flow from plate to plate till the charge on both the plates becomes zero.
Chapter 20 Electric Potential and Electrical Potential Energy Q.9P
The Electric Potential of the Earth The Earth has a vertical electric field with a magnitude of approximately 100 V/m near its surface. What is the magnitude of the potential difference between a point on the ground and a point on the same level as the top of the Washington Monument (555 ft high)?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.10CQ
It would be unwise to unplug a television set, take off the back, and reach inside. The reason for the danger is that if you happen to touch the terminals of a high-voltage capacitor you could receive a large electrical shock—even though the set is unplugged. Why?
Solution:
Even after the television set is unplugged, the charge in the high voltage capacitor will remain there. So, when you come in contact with this capacitor you will receive a large electric shock.
Chapter 20 Electric Potential and Electrical Potential Energy Q.10P
A uni form electric field with a magnitude of 6350 N/C points in the positive x direction. Find the change in electric potential energy when a +12.5-μC charge is moved 5.50 cm in (a) the positive x direction, (b) the negative x direction, and (c) the positive y direction.
Solution:
Chapter 20 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 3.0 × 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:
Chapter 20 Electric Potential and Electrical Potential Energy Q.12CQ
We say that a capacitor stores charge, 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 zero?
Solution:
Though the net charge of a capacitor is zero, charge of opposite signs is stored in two different locations. So we can say that a capacitor stores opposite charges separately and even has the energy needed to cause the separation.
Chapter 20 Electric Potential and Electrical Potential Energy Q.12P
Solution:
Chapter 20 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 not zero even if the plates of the parallel-plate capacitor are uncharged because the term CAPACITANCE defines the capacity of the capacitor which will not be zero.
Chapter 20 Electric Potential and Electrical Potential Energy Q.13P
A Charged Battery A typical 12-V car 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 rest?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.14P
IP BIO The Sodium Pump Living cells actively “pump” positive sodium ions (Na+) from inside the 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 V higher outside the cell than inside the cell, and that the cell membrane is 0.10 μm thick, (a) calculate the work that must be done (in joules) to move one sodium ion from inside the cell to outside. (b) If the thickness of the cell membrane is increased, does your answer to part (a) increase, decrease, or stay the same? Explain. (It 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 Electric Potential and Electrical Potential Energy Q.15P
Solution:
Chapter 20 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 rest at point B, however, its kinetic energy when it reaches point C is KB = 2KA. What are (a) the electric potential at point C and (b) the kinetic energy KA?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.17P
CE Predict/Explain An electron is released from rest in a region of space with a nonzero electric field, (a) As the electron
moves, does the electric potential energy of the system increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. Because the electron has a negative charge its electric potential energy doesn’t decrease, as one might expect, but increases instead.
II. As the electron begins to move, its kinetic energy increases. The increase in kinetic energy is equal to the decrease in the electric potential energy of the system.
III. The electron will move perpendicular to the electric field, and hence its electric potential energy will remain the same.
Solution:
(a) The electron potential 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 increase in kinetic energy of electron is equal to the decrease in potential energy of system. So best explanation is (II)
Chapter 20 Electric Potential and Electrical Potential Energy Q.18P
Calculate the speed of (a) a proton and (b) an electron after each particle accelerates from rest through a potential difference of 275 V.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.19P
The electrons in a TV picture tube are accelerated from rest through a potential difference of 25 kV. What is the speed of the electrons after they have been accelerated by this potential difference?
Solution:
Chapter 20 Electric 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 become significant.)
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.21P
IP A particle with a mass of 3.8 g and a charge of +0.045 μC is released from rest at point A in Figure 20-20. (a) In which direction will this charge move? (b) What speed will it have after moving through a distance of 5.0 cm? The electric field has a magnitude of 1200 N/C. (c) Suppose the particle continues moving for another 5.0 cm. Will its increase in speed for the second 5.0 cm be greater than, less than, or equal to its increase in speed in the first 5.0 cm? Explain.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.22P
A proton has an initial speed of 4.0 × 105 m/s. (a) What potential difference is required to bring the proton to rest? (b) What potential difference is required to reduce the initial speed of the proton by a factor of 2? (c) What potential difference is required to reduce the initial kinetic energy of the proton by a factor of 2?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.23P
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.24P
CE The charge q1 in Figure 20-22 has the value +Q. (a) What value must q2 have if the electric 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 zero? Explain.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.25P
CE It is given that the electric potential is zero 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 electric potential at point A positive, negative, or zero? Explain, (c) Is the electric potential at point B positive, negative, or zero? Explain.
Solution:
The above value shows the net electric potential at point B is negative. This is because the point B is closer to the negative charge 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 charge.
Hence, the net electric potential at point B is .negative
Chapter 20 Electric Potential and Electrical Potential Energy Q.26P
The electric potential 1.1 m from a point charge q is 2.8 × 104 V. What is the value of q?
Solution:
Chapter 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) (−3.0 m, 0); and (c) (3.0 m,-3.0 m)
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.28P
The Bohr Atom The hydrogen atom consists of one electron and one proton, hi the Bohr model of the hydrogen atom 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’s orbit?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.29P
How far must the point charges q1 = +7.22 μC and q2 = −26.1 μC be separated for the electric potential energy of the system to be −126 J?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.30P
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.31P
IP Point charges +4.1 μC and −2.2μC are placed on the x axis at (11 m, 0) and (−11 m, 0), respectively, (a) Sketch the electric potential on the x axis for this system, (b) Your sketch should show one point on the x axis between the two charges where the potential vanishes. Is this point closer to the +4.1-−μC charge or closer to the −2.2-μC charge? Explain, (c) Find the point referred to in part (b).
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.32P
IP (a) In the previous problem, find the point to the left of the negative charge where the electric potential vanishes, (b) Is the electric field at the point found in part (a) positive, negative, or zero? Explain.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.33P
A dipole is formed by point charges +3.6 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 system. (b) At what positions on the x axis does the potential have the value 7.5 × 105 V?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.34P
A charge of 3.05 μC is held fixed at the origin. A second charge of 3.05 μC is released from rest at the position (1.25 m, 0.570 m). (a) Tf the mass of the second charge is 2.16 g, what is its speed when it moves infinitely far from the origin? (b) At what distance from the origin does the second charge attain half the speed it will have at infinity?
Solution:
Therefore the second particle attains half of the speed at infinity at a distance of 1.84m from the origin.
Chapter 20 Electric Potential and Electrical Potential Energy Q.35P
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.36P
A charge of -2.205 μC is located at (3.055 m, 4.501 in), and a charge of 1.800 μC is located at (−2.533 m, 0). (a) Find the electric potential at tine origin, (b) There is one point on the line connecting these two charges where the potential is zero. Find this point.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.37P
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.38P
How much work must be done to move the three charges in Figure 20-24 infinitely far from one another?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.39P
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.40P
A square of side a has a charge +Q at each corner. What is the electric potential energy of this system of charges?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.41P
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.42P
CE Predict/Explain A positive charge is moved from one location on an equipotential to another point on the same equipotential. (a) Is the work done on the charge positive, negative, or zero? (b) Choose the best explanation from among the following: I. The electric field is perpendicular to an equipotential, therefore the work done in moving along an equipotential is zero.
I. Because the charge is positive the work done on it is also positive.
II. It takes negative work to keep the positive charge from accelerating as it moves along the equipotential.
Solution:
(a) Given,
A positive charge is moved from one location to another location in which both the locations are at same equipotential. Since the positive charge is moving in same equipotential there is no work done by the positive charge because of same equipotential. So work done in moving the positive charge from one place to another place is zero.
(b) The electric field is perpendicular to an equipotential therefore the work done in moving along equipotential is zero.
Therefore is the best explanation.
Chapter 20 Electric Potential and Electrical Potential Energy Q.43P
CE Predict/Explain (a) Is the electric potential at point 1 in Figure 20-19 greater than, less than, or equal to the electric potential at point 3? (b) Choose the best explanation from among the following:
I. The electric field lines point to the right, indicating that the electric potential is greater at point 3 than at point 1.
II. The value of the electric potential is large where the electric field lines are close together, and small where they are widely spaced. Therefore, the electric potential is the same at points 1 and 3.
III· The electric potential decreases as we move in the direction of the electric field, as shown in Figure 20-3. Therefore, the electric potential is greater at point 1 than at point 3.
Solution:
(a) The electric potential at point 1 is greater than the electric potential at point 3.
(b) We know that the direction of electric field is from high potential to low potential. Therefore the electric potential will decrease when we move in the field direction. In the figure the direction of electric field is from point 1 to point 3. So the electric potential at point 1 is greater than the electric potential at point 3.
Therefore option III is the best explanation.
Chapter 20 Electric Potential and Electrical Potential Energy Q.44P
CE Predict/Explain Imagine sketching a large number of equipotential surfaces in Figure 20-19, with a constant difference in electric potential between adjacent surfaces, (a) Would the equipotentials at point 2 be more closely spaced, be less closely spaced, or have the same spacing as equipotentials at point 1? (b) Choose the best explanation from among the following:
I. When electric field lines are close together, the corresponding equipotentials are far apart.
II. Equipotential surfaces, by definition, always have equal spacing between them.
III. The electric field is more intense at point 2 than at point 1, which means the equipotential surfaces are more closely spaced in that region.
Solution:
(a) When we draw large number of equipotential surfaces with constant potential difference between adjacent surfaces, the equipotentials at point 2 are more closely spaced as equipotentials at point1.
Comment
(b) From the figure it is clear that the electric field is more intense near point 2 than near point 1, because the field lines are packed more closely together near point 2. This means, in turn, that the electric potential changes more rapidly with position at point 2. As a result, the spacing between equipotential surfaces at point 2 is less than the spacing between equipotential surfaces at point 1.
Therefore option III is the best explanation.
Chapter 20 Electric Potential and Electrical Potential Energy Q.45P
Two point charges are on the x axis. Charge 1 is +q and is located at x = −1.0 m; charge 2 is −2q and is located at x = 1.0 m. Make 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 case, indicate the direction in· which the potential increases.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.46P
Two point charges are on the x axis. Charge 1 is +q and is located at x = −1.0 m; charge 2 is +2q and is located at x − 1.0 m. Make 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 case, indicate the direction in which the potential increases.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.47P
Solution:
Chapter 20 Electric Potential and Electrical 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
move in the positive x direction, does the clectric potential increase or decrease? Explain, (c) What is the distance between the +14-V and the +16-V equipotentials?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.49P
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.50P
A 0.40−μF capacitor is connected to a 9.0-V battery. How much charge is on each plate of the capacitor?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.51P
It is desired that 5.8 μC of charge be stored on each plate of a 3.2-μ F capacitor. What potential difference is required between the plates?
Solution:
Chapter 20 Electric Potential and Electrical 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 9.0 V?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.53P
A parallel-plate capacitor is made from two aluminum-foil sheets, each 6.3 cm wide and 5.4 m 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 constant of Teflon is 2.1.)
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.54P
parallel-plate capacitor is constructed 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 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 between the plates when the charge on the capacitor plates is 4.7 μC? (b) Will your answer to part (a) increase, decrease, or stay the same if the dielectric constant is increased? Explain, (c) Calculate the potential difference for the case where the dielectric constant is 4.0.
Solution:
Chapter 20 Electric 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 distance of 1.5 mm. (a) What radius must the plates have if the capacitance of this capacitor is to be 1.0 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? Explain, (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 Energy Q.57P
A parallel-plate capacitor has plates of area 3.45 × 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 Electric 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) Find the magnitude of the charge 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 between the plates is increased? Explain, (c) Calculate the magnitude of the charge on the plates if the separation is 0.90 mm.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.59P
Suppose that after walking across a carpeted floor you reach for a doorknob and just before you touch it a spark jumps 0.50 cm from your finger to the knob. Find the minimum voltage needed between your finger and the doorknob to generate this spark.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.60P
(a) What plate area is required if an air-filled, parallel-plate capacitor with a plate separation of 2.6 mm is to have a capacitance of 22 pF? (b) What is the maximum voltage that can be applied to this capacitor without causing dielectric breakdown?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.61P
Lightning As a crude model for lightning, consider the ground to be one plate of a parallel-plate capacitor and a cloud at an altitude of 550 m to be the other plate. Assume the surface area of the cloud to be the same as 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 two aluminum-foil sheets, each 3.00 cm wide and 10.0 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 can be stored in this capacitor? (The dielectric constant of mica is 5.4, and its dielectric strength is 1.00 x 108V/m.)
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.63P
Calculate the work done by a 3.0-V battery as it charges a 7.8-μF capacitor in the flash unit of a camera
Solution:
Chapter 20 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 V. What is the capacitance of this device?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.65P
IP BIO Cell Membranes The membrane of a living cell can be approximated by 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 4.5. (a) What is the energy stored in such a cell membrane if the potential difference across it is 0.0725 V? (b) Would your answer to part (a) increase, decrease, or stay the same if the thickness of the 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 1.5-V battery. After being charged, the capacitor is connected to a small electric motor. Assuming 100% efficiency, (a) to what height can the motor lift a 5.0-g mass? (b) What initial voltage must the capacitor have if it is to lift a 5.0-g mass through a height of 1.0 cm?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.67P
Find the electric energy density between the plates of a 225-μF parallel-plate capacitor. The potential difference between the plates is 345 V, and the plate separation is 0.223 mm.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.68P
What electric field strength would store 17.5 Jof energy in every 1.00 mm3 of space?
Solution:
Chapter 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 ready for operation, the potential difference between the capacitor plates is 330 V. (a) What is the magnitude of the charge on each plate of the fully charged capacitor? (b) Find the energy stored in the “charged-up” flash 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 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 4.50 mm. How much energy is stored in the capacitor now? (c) How much work is required to increase the separation of the plates from 2.25 mm to 4.50 mm? Explain your reasoning.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.71GP
CE A proton is released from rest in a region of space with a nonzero electric field. As the proton moves, does it experience an increasing or decreasing electric 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 non-zero electric field.
In electrostatics, the positively charged region is treated as higher potential region and the negatively charged region is treated as lower potential region. The electric fields lines always 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 electric field that is it travels towards the lower potential region. Therefore, the proton travels experience decreasing electric potential in the non-zero electric field region.
Chapter 20 Electric Potential and Electrical Potential Energy Q.72GP
CE Predict/Explain A proton is released from rest in a region of space with a nonzero electric field, (a) As the proton moves, does the electric potential energy of the system increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. As the proton begins to move, its kinetic energy increases. The increase in kinetic energy is equal to the decrease in the electric potential energy of the system.
II. Because the proton has a positive charge, its electric potential energy will always increase.
III. The proton will move perpendicular to the electric field, and hence its electric potential energy will remain the same.
Solution:
(a)
If the proton released from rest in the region of space with non-zero electric field it gains kinetic energy.
From the conservation of energy, total energy (Sum of kinetic energy and electric potential energy) of the system is constant.
Then the electric potential 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 energy are equal to the decrease in the electric potential energy of the system.
ANS: I
Chapter 20 Electric Potential and Electrical 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 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 electric potential energy of the system increase, decrease, or stay the same? Explain.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.74GP
CE The plates of a parallel-plate capacitor have constant charges of +Q and-Q. Do the following quantities increase, decrease, or remain the same as the separation of the plates is increased? (a) The electric field between the plates; (b) the potentiell difference between the plates; (c) the capacitance; (d) the energy stored in the capacitor.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.75GP
CE A parallel-plate capacitor is connected to a battery that maintains a constant potential difference V between the plates. If the plates of the capacitor are pulled farther apart, do the following 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 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. Do the following quantities increase, decrease, or remain the same as a dielectric is inserted between the plates? (a) The electric field between the plates; (b) the potential difference between the plates; (c) the capacitance; (d) the energy stored in the capacitor.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.77GP
CE A parallel-plate capacitor is connected to a battery that maintains a constant potential difference V between the plates. If a dielectric is inserted between the plates of the capacitor, do the following quantities increase, decrease, or remain the same? (a) The electric field between,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 Energy Q.78GP
Find the difference in electric potential, ΔV = VB — VA between the points A and B for the following cases: (a) The electric field does 0.052 J of work as you move a +5.7-μC charge from A to B. (b) The electric field does -0.052 J of work as you move a −5.7-μC charge from A to B. (c) You perform 0.052 J of work as you slowly move a +5.7-μC charge from A to B.
Solution:
Chapter 20 Electric Potential and Electrical 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 connected to a battery that maintains a constant potential difference between the plates. If the spacing between the plates is doubled, how is the magnitude of charge on the plates affected?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.81GP
CE Two point charges arc placed on the x axis. The charge +2q is at x = 1.5 m, and the charge —q is at x = −1.5 m. (a) There is a point on the x axis between the two charges where the electric potential is zero. Where is this point? (b) The electric potential also vanishes at a point in one of the following regions: region 1, x between 1.5 m and 5.0 m; region 2, x between −1.5 m and −3.0 m; region 3, x between −3.5 m and −5.0 m. Identify the appropriate region, (c) Find the value of x referred to in part (b).
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.82GP
A charge of 24.5 μC is located at (4.40 m, 6.22 m), and a charge of −11.2 μC is located at (−4.50 m, 6.75 m). What charge must be located at (2.23 m, −3.31 m) if the electric potential is to be zero 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 amount 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 as the ionization energy of hydrogen.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.84GP
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.85GP
Repeat Problem 84 for the case where both charges arc +1.2 μC.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.86GP
How much work is required to bring three protons, initially infinitely far apart, to a configuration where each proton is 1.5 × 10-15 m from the other two? (This is a typical separation for protons in a nucleus.) ·
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.87GP
A point charge Q = +87.1 μC is held fixed at the origin. A second point charge, with mass m = 0.0576 kg and charge q = −2.87 μC, is placed at the location (0.323 m, 0). (a) Find the clectric potential energy of this system of charges, (b) If the second charge is released from rest, what is its speed when it reaches the point (0.121 m, 0)?
Solution:
Chapter 20 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 2.7 mm and a uniformly distributed positive charge of 1.8 × 10-15 C. Like a rocket blasting off from the Earth, 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:
Chapter 20 Electric Potential and Electrical Potential Energy Q.89GP
Quark Model of the Neutron According to the quark model of fundamental particles, neutrons—the neutral particles in an atom’s nucleus—are composed of three quarks. Two of these quarks are “down” quarks, each with a charge of —e/3; the third quark is an “up” quark, with a charge of +2e/3. This gives the neutron a net charge of zero. What is the electric potential energy of these three quarks, assuming they are equidistant from one another, with a separation distance of 1.3 × 10-15 m? (Quarks are discussed in Chapter 32.)
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.90GP
A parallel-plate capacitor is charged to an electric potential of 325 V by moving 3.75 × 1016 electrons from one plate to the other. How much work is done in charging the capacitor?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.91GP
IP The three charges shown in Figure 20-25 are held in place as a fourth charge, q, is brought from infinity to the point P. The charge q starts at rest at infinity and is also at rest when it is placed at the point P. (a) If q is a positive charge, is the work required to bring it to the point P positive, negative, or zero? Explain. (b) Find the value of (/ if the work needed to bring it to point P is −1.3 × 10-11 J.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.92GP
(a) In Figure 20-28 we see that the electric potential increases by 10.0 V as one moves 4.00 cm in the positive x direction. Use this information to calculate the x component of the electric field. (Ignore the y direction for the moment.) (b) Apply the same reasoning as 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 20 Electric Potential and Electrical Potential Energy Q.93GP
IP BIO Electric Catfish The electric catfish (Malapterurs electricus) is an aggressive fish, 1.0 m in length, found today in tropical Africa (and depicted in Egyptian hieroglyphics). The catfish is capable of generating jolts of electricity up to 350 V by producing a positively charged region of muscle near the head and a negatively charged region near the tail, (a) For the same amount of charge, can the catfish generate a higher voltage by separating the charge from one end of its body to the other, as it does, or from one side of the body to the other? Explain, (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 × 10-2 m2, separation 1.0 m, and filled with a dielectric with a dielectric constant K = 95.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.94GP
As a +6.2-μC charge moves along the x axis from x = 0 to x = 0.70 m, the electric potential it experiences is shown in Figure 20-21. Find the approximate location(s) of the charge when its electric potential energy is (a) 2.6 × 10—5 J and (b) 4.3 × 10—5 J.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.95GP
IP Computer Keyboards Many computer keyboards operate on the principle of capacitance. As shown in Figure 20-16, each key forms a small parallel-plate capacitor whose separation is reduced when the key is depressed, (a) Does depressing a key increase or decrease its capacitance? Explain, (b) Suppose the plates for each key have an area of 47.5 mm2,and an initial separation of 0.550 mm. In addition, let the dielectric have a dielectric constant of 3.75. If the circuitry of the computer can detect a change in capacitance of 0.425 pF, what is the minimum distance a key must be depressed to be detected?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.96GP
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.97GP
BIO Cell Membranes and Dielectrics Many cells in the body have a cell membrane whose inner and outer surfaces carry opposite charges, just like the plates of a parallel-plate capacitor. Suppose a typical cell membrane has a thickness of 8.1 × 10-9 m, and its inner and outer surfaces carry charge densities of −0.58 × 10 3 C/m2 and +0.58 × 10-3 C/m2, respectively. In addition, assume that the material in the cell membrane has a dielectric constant of 5.5. (a) Find the direction and magnitude of the electric field within the cell membrane, (b) Calculate the potential difference between the inner and outer walls of the membrane, and indicate which wall of the membrane has the higher 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 zero net charge was dropped from rest at a height of 1.00 m. The ball landed 0.552 s later. Next, the ball was given a net charge of 7.75 μC and dropped in the same way from the same height. This time the ball fell for 0.680 s before landing. What is the electric potential at a height of 1.00 m above the ground on this planet, given that the electric potential at ground level is zero? (Air resistance can be ignored.)
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.99GP
Rutherford’s Planetary Model of the Atom In 1911, Ernest Rutherford developed a planetary model of the atom, 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 tIn s experiment, they fired alpha particles with an initial speed of 1.75 × 107 m/s at a tIn n sheet of gold. (Alpha particles are obtained from certain radioactive decays. They have a charge of +2e and a mass of 6.64 × 10-27 kg.) Flow close can the alpha particles get to a gold nucleus (charge = +79e), assuming the nucleus remains stationary? (This calculation sets an upper limit on the size of the gold nucleus. See Chapter 31 for further details.)
Solution:
The work energy theorem states that the total work done of a system is equal to its change in kinetic energy.
Chapter 20 Electric Potential and Electrical Potential Energy Q.100GP
IP (a) One of the — Q charges in Figure 20-26 is given an outward “kick” that sends it off with an initial speed V0 wIn le the other three charges are held at rest. If the moving charge has a mass m, what is its speed when it 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 two +Q charges, is its speed greater than, less than, or the same as the speed found in part (a)? Explain.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.101GP
Figure 20-30 shows a charge q = +6.77 μC with a mass m = 0.071 kg suspended by a thread of length L = 0.022 m between the plates of a capacitor, (a) Plot the electric potential energy of the system as 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 part (a) for
tine case of the gravitational potential energy of the system, (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:
Chapter 20 Electric Potential and Electrical Potential Energy Q.102GP
The electric potential a distance r from a point charge q is 2.70 × 104 V. One meter farther away from the charge the potential is 6140 V. Find the charge q and the initial distance r.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.103GP
Referring to Problem 84, calculatc and plot the electric potential on the circle centered at (0.50 m, 0). Give your results in terms of the angle ×, defined as follows: θ is the angle measured counterclockwise from a vertex at the center of the circle, with θ = 0 at point C.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.104GP
When the potential difference between the plates of a capacitor is increased by 3.25 V, the magnitude of the charge on each plate increases by 13.5 μC. What is the capacitance of this capacitor?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.105PP
The electric potential a distance r from a point charge q is 155 V, and the magnitude of the elcctric field is 2240 N/C. Find the values of q and r.
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.106PP
Electric eels produce an electric field witIn n their body. In which direction does the electric field point?
A. toward the head
B. toward the tail
C. upward
D. downward
Solution:
As the muscle cells called electro plaques producing each of 0.15V, these electro plaques are producing voltage in the body of eel together by producing the positive charge at head and negative charge at tail.
So electric field in the eel body is directed toward the tail.
So the correct option is (B)
Chapter 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 area 1.8 × 10-2 m2 separated by 2.0 m and filled with a dielectric whose dielectric constant 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. 1.5 ×10-11 F
D. 9.3 ×10-8 F
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.108PP
In terms of the parallel-plate model of the previous problem, how much charge does an electric eel generate at each end of its body when it produces a voltage of 650 V?
A. 1.2 ×10-14C
B. 5.2 ×10-11 C
C. 4.9×10-9 C
D. 6.1 ×10-5C
Solution:
Chapter 20 Electric Potential and Electrical 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. 1.8 ×10-17J
B. 1.7 ×10-8J
C. 1.6×10-6J
D. 2.0×10-2J
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.110PP
IP Referring to Example 20-3 Suppose the charge -2q at x = 1.00 m is replaced with a charge -3q, where q = 4.11 ×10-9 C. The charge +q is at the origin, (a) Is the electric potential positive, negative, or zero at the point x = 0.333 m? Explain. (b) Find the point between x = 0 and x = 1.00 m where the electric potential vanishes, (c) Is there a point in the region x < 0 where the clectric potential passes through zero?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.111IP
Referring to Example 20-3 Suppose we can change 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 electric potential vanishes at x = 0.500 m? (b) With the location of −2q found in part (a), where does the clectric potential pass through zero in the region x < 0?
Solution:
Chapter 20 Electric Potential and Electrical Potential Energy Q.112IP
IP Referring to Example 20-3 Suppose the charge +q at the origin is replaced with a charge +5q, where q = 4.11 × 10-9 C. The charge -2q is still at x = 1.00 m. (a) Is there a point in the region x<0 where the electric potential passes through zero? (b) Find the location between x = 0 and x = 1.00 m where the electric potential passes through zero, (c) Find the location in the region x > 1.00 m where the electric potential passes through zero.
Solution:
