Chapter 17 Homework

1) If the result of your calculation of a quantity has SI units kg · m2/(s2 · C), that quantity could be
A) an electric field strength.
B) a capacitance
C) an electric potential energy.
D) an electric potential difference.
E) a dielectric constant.
2) If the result of your calculation of a quantity has SI units of kg   m/(s2 · C), that quantity could be
A) a dielectric constant.
B) an electric field strength.
C) a capacitance
D) an electric potential energy.
E) an electric potential difference
3) As a proton moves in the direction the electric field lines
A) it is moving from low potential to high potential and gaining electric potential energy.
B) it is moving from low potential to high potential and losing electric potential energy.
C) it is moving from high potential to low potential and gaining electric potential energy.
D) it is moving from high potential to low potential and losing electric potential energy.
E) both its electric potential and electric potential energy remain constant.

4) As an electron moves in the direction the electric field lines
A) it is moving from low potential to high potential and gaining electric potential energy.
B) it is moving from low potential to high potential and losing electric potential energy.
C) it is moving from high potential to low potential and gaining electric potential energy.
D) it is moving from high potential to low potential and losing electric potential energy.
E) both its electric potential and electric potential energy remain constant.

5) As a proton moves in a direction perpendicular to the electric field lines
A) it is moving from low potential to high potential and gaining electric potential energy.
B) it is moving from low potential to high potential and losing electric potential energy.
C) it is moving from high potential to low potential and gaining electric potential energy.
D) it is moving from high potential to low potential and losing electric potential
E) both its electric potential and electric potential energy remain constant.

6) A proton is accelerated from rest through a potential difference V0 and gains a speed v0. If it were accelerated instead through a potential difference of 2V0, what speed would it gain?
A) 2v0                 B) 8v0                 C) v0√2                 D) 4v0

7) If the electric potential at a point in space is zero, then the electric field at that point must be
A) negative.
B) uniform.
C) zero.
D) positive.
E) impossible to determine based on the information given.

8) The electric potential at a distance of 4 m from a certain point charge is 200 V relative to infinity. What is the potential (relative to infinity) at a distance of 2 m from the same charge?
A) 400 V         B) 200 V         C) 100 V         D) 600 V         E) 50 V

9) The potential (relative to infinity) at the midpoint of a square is 3.0 V when a point charge of +Q is located at one of the corners of the square. What is the potential (relative to infinity) at the center when each of the other corners is also contains a point charge of +Q?
A) 3.0 V             B) 12 V                 C) 0 V                 D) 9.0 V

10) Four charged particles (two having a charge +Q and two having a charge -Q) are arranged in the xy-plane as shown in the figure. The charges are all equidistant from the origin. The amount of work required to move a positively charged particle from point P to point O (both of which are on the z-axis) is

A) positive.                         B) negative.
C) zero.                         D) depends on the path it moves along.

11) A region of space contains a uniform electric field, directed toward the right, as shown in the figure. Which statement about this situation is correct?

A) The potential at point A is the highest, the potential at point B is the second highest, and the potential at point C is the lowest.
B) The potential at all three locations is the same.
C) The potential at points A and B are equal, and the potential at point C is lower than the potential at point A.
D) The potentials at points A and B are equal, and the potential at point C is higher than the potential at point A.

12) Two ideal parallel-plate capacitors are identical in every respect except that one has twice the plate area of
the other. If the smaller capacitor has capacitance C, the larger one has capacitance
A) C.                 B) 4C.                 C)C/2.                 D) 2C.

13) When a certain capacitor carries charges of ±10 μC on its plates, the potential difference cross the plates is 25 V. Which of the following statements about this capacitor are true? (There could be more than one correct choice.)
A) If we double the charges on the plates to ±20 μC, the capacitance of the capacitor will not change.
B) If we double the charges on the plates to ±20 μC, the capacitance of the capacitor will also double.
C) If we double the charges on the plates to ±20 μC, the potential difference across the plates will also double.
D) If we double the charges on the plates to ±20 μC, the potential difference across the plates will decrease by a factor of two.

14) An ideal parallel-plate capacitor having circular plates of diameter D that are a distance d apart stores energy U when it is connected across a fixed potential difference. If you want to triple the amount of energy stored in this capacitor by changing only the size of its plates, the diameter should be changed to
A) 9D.             B) 3D.             C)….        D)……            E)…..

15) Doubling the capacitance of a capacitor that is holding a constant charge causes the energy stored in that capacitor to
A) decrease by one-half.                 B) quadruple.
C) double.                        D) decrease by one-fourth.

16) At a distance d from a point charge Q, the energy density in its electric field is u. If we double the charge, what is the energy density at the same point?
A) u 2             B) 8u             C) 2u             D) 16u             E) 4u

17) How much kinetic energy does a proton gain if it is accelerated, with no friction, through a potential difference of 1.00 V? The proton is 1836 times heavier than an electron, and e = 1.60 × 10-19 C.

18) How much work must we do on an electron to move it from point A, which is at a potential of +50V, to point B, which is at a potential of -50 V, along the semicircular path shown in the figure? Assume the system is isolated from outside forces. (e = 1.60 × 10-19 C)
 

19) If an electron is accelerated from rest through a potential difference of 1500 V, what speed does it reach? (e =1.60 × 10-19 C , melectron = 9.11 × 10-31 kg)

20) How much work is needed to carry an electron from the positive terminal to the negative terminal of a 9.0-V battery. (e = 1.60 × 10-19 C , melectron = 9.11 × 10-31 kg)

21) If it takes 50 J of energy to move 10 C of charge from point A to point B, what is the magnitude of the
potential difference between points A and B?

22) A sphere with radius 2.0 mm carries a +2.0 μC charge. What is the potential difference, VB – VA, between point B, which is 4.0 m from the center of the sphere, and point A, which is 6.0 m from the center of the sphere? (k = 1/4πε0 = 9.0 × 109 N · m2/C2)

23) Two 3.0 μC charges lie on the x-axis, one at the origin and the other at 2.0 m. What is the potential (relative to infinity) due to these charges at a point at 6.0 m on the x-axis? (k = 1/4πε0 = 9.0 × 109 N · m2/C2)

24) A +4.0-μC and a -4.0-μC point charge are placed as shown in the figure. What is the potential difference between points A and B? (k = 1/4πε0 = 9.0 × 109 N· m2/C2)

25) A very small 4.8-g particle carrying a charge of +9.9 μC is fired with an initial speed of 8.0 m/s directly toward a second small 7.8-g particle carrying a charge of +5.2 μC. The second particle is held fixed throughout this process. If these particles are initially very far apart, what is the closest they get to each other? (k = 1/4πε0 = 9.0 × 109 N · m2/C2)

26) A point charge of +3.00 μC and a second charge Q are initially very far apart. If it takes 29.0 J of work to bring
them to a final configuration in which the +3.00-μC charge is at the point x = 1.00 mm, y = 1.00 mm, and the
second charge Q is at the point x = 1.00 mm, y = 3.00 mm, find the magnitude of the charge Q. (k = 1/4πε0 =
8.99 × 109 N · m2/C2)

27) A +5.0-nC charge is at the point (0.00 m, 0.00 m) and a -2.0-nC charge is at (3.0 m, 0.00 m). What work is required to bring a 1.0-nC charge from very far away to point (0.00 m, 4.0 m)? (k = 1/4πε0 = 9.0 × 109 N · m2/C2)

28) The potential difference between two square parallel plates is 4.00 V. If the plate separation is 6.00 cm and they each measure 1.5 m by 1.5 m, what is the magnitude of the electric field between the plates?

29) A spherical oil droplet with nine excess electrons is held stationary in an electric field between two large horizontal plates that are 2.25 cm apart. The field is produced by maintaining a potential difference of 0.3375 kV across the plates, and the density of the oil is 824 kg/m3. What is the radius of the oil drop? (e = 1.60 × 10-19 C)

30) The equipotential surfaces for two point charges are shown in the figure, with the value of potential marked
on the line for each surface.
(a) What is the potential difference, VG – VD, between points G and D?
(b) What is the potential difference, VA – VG, between points A and G?

31) What charge accumulates on the plates of a 2.0-μF air-filled capacitor when it is charged until the potential difference across its plates is 100 V?

32) The potential difference between the plates of an ideal air-filled parallel-plate capacitor with a plate separation of 6.0 cm is 60 V. What is the strength of the electric field between the plates of this capacitor?

33) An air-filled 20-μF capacitor has a charge of 60 μC on its plates. How much energy is stored in this capacitor?

34) When a 6.00-μF air-filled capacitor has a charge of ±40.0 μC on its plates, how much potential energy is stored in this capacitor?

35) A parallel-plate capacitor consists of two parallel, square plates having dimensions 1.0 cm by 1.0 cm. The plates are separated by 1.0 mm, and the space between them is filled with Teflon, which has a dielectric constant of 2.1. What is the capacitance of this capacitor? (ε0 = 8.85 × 10-12 C2/N · m2)