Deck 17: Electric Potential

Question 1

Write the word or phrase that best completes each statement or answers the question.
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) $\frac { D } { 3 }$
B) $3 D$ .
C) $D \sqrt { 3 }$
D) $\frac { \mathrm { D } } { \sqrt { 3 } }$
E) 9D.

Answer 1

C

Question 2

Write the word or phrase that best completes each statement or answers the question.
If an electron is accelerated from rest through a potential difference of $1500 \mathrm {~V}$ , what speed does it reach? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

A) $1.5 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$
B) $2.3 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$
C) $1.1 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$
D) $1.9 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$

Answer 2

B

Question 3

Write the word or phrase that best completes each statement or answers the question.
A proton with a speed of $2.0 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$ accelerates through a potential difference and thereby increases its speed to $4.0 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$ . Through what magnitude potential difference did the proton accelerate? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$

A) $840 \mathrm {~V}$
B) $1000 \mathrm {~V}$
C) $100 \mathrm {~V}$
D) $210 \mathrm {~V}$
E) $630 \mathrm {~V}$

Answer 3

E

Question 4

Write the word or phrase that best completes each statement or answers the question.
Four charged particles (two having a charge $+ Q$ and two having a charge $- Q$ ) are arranged in the $x y$ -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 in which the charged is moved.

Question 5

Write the word or phrase that best completes each statement or answers the question.
Four charged particles (two having a charge $+ Q$ and two having a charge $- Q$ ) are arranged in the $x y$ -plane, as shown in the figure. These particles are all equidistant from the origin. The electric potential (relative to infinity) at point $\mathrm { P }$ on the $z$ -axis due to these particles, is

A) negative.
B) positive.
C) zero.
D) impossible to determine based on the information given.

Question 6

Write the word or phrase that best completes each statement or answers the question.
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 all three locations is the same.
B) The potential at points $A$ and $B$ are equal, and the potential at point $C$ is lower than the potential at point $A$ .
C) The potentials at points $A$ and $B$ are equal, and the potential at point $C$ is higher than the potential at point A.
D) The potential at point $\mathrm { A }$ is the highest, the potential at point $\mathrm { B }$ is the second highest, and the potential at point $C$ is the lowest.

Question 7

Write the word or phrase that best completes each statement or answers the question.
A proton that is initially at rest is accelerated through an electric potential difference of magnitude $500 \mathrm {~V}$ . What speed does the proton gain? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m \right.$ proton $\left. = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$

A) $1.1 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$
B) $3.1 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$
C) $2.2 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$
D) $9.6 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$

Question 8

Write the word or phrase that best completes each statement or answers the question.
When a certain capacitor carries charges of $\pm 10 \mu \mathrm { C }$ on its plates, the potential difference cross the plates is $25 \mathrm {~V}$ . 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 $\pm 20 \mu \mathrm { C }$ , the potential difference across the plates will decrease by a factor of two.
B) If we double the charges on the plates to $\pm 20 \mu \mathrm { C }$ , the capacitance of the capacitor will also double.
C) If we double the charges on the plates to $\pm 20 \mu \mathrm { C }$ , the potential difference across the plates will also double.
D) If we double the charges on the plates to $\pm 20 \mu \mathrm { C }$ , the capacitance of the capacitor will not

Question 9

Write the word or phrase that best completes each statement or answers the question.
If the electric field between the plates of a given air-filled capacitor is weakened by removing charge from the plates, the capacitance of that capacitor

A) does not change.
B) decreases.
C) increases.
D) It cannot be determined from the information given.

Question 10

Write the word or phrase that best completes each statement or answers the question.
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) $4 C$ .
B) $2 \mathrm { C }$ .
C) $C / 2$ .
D) $\mathrm { C }$ .

Question 11

Write the word or phrase that best completes each statement or answers the question.
How much kinetic energy does a proton gain if it is accelerated, with no friction, through a potential difference of $1.00 \mathrm {~V}$ ? The proton is 1836 times heavier than an electron, and $e = 1.60 \times10^{-19}$ C.

A) $1836 \mathrm { eV }$
B) $1.00 \mathrm {~J}$

C) $1836 \mathrm {~J}$

D) $1.60 \times 10 ^ { - 19 } \mathrm { eV }$

E) $1.00 \mathrm { eV }$

Question 12

Write the word or phrase that best completes each statement or answers the question.
A proton is accelerated from rest through a potential difference $V _ { 0 }$ and gains a speed $v _ { 0 }$ . If it were accelerated instead through a potential difference of $2 V _ { 0 }$ , what speed would it gain?

A) $2 v _ { 0 }$
B) $8 v _ { 0 }$
C) $v 0 \sqrt { 2 }$
D) $4 v _ { 0 }$

Question 13

Write the word or phrase that best completes each statement or answers the question.
A tiny particle with charge $+ 5.0 \mu \mathrm { C }$ is initially moving at $55 \mathrm {~m} / \mathrm { s }$ . It is then accelerated through a potential difference of $500 \mathrm {~V}$ . How much kinetic energy does this particle gain during the period of acceleration?

A) $2500 \mathrm {~J}$
B) $2.5 \times 10 ^ { - 3 } \mathrm {~J}$
C) $1.0 \times 10 ^ { 4 } \mathrm {~J}$
D) $100 \mathrm {~J}$

Question 14

Write the word or phrase that best completes each statement or answers the question.
If the result of your calculations for a quantity has $\mathrm { SI }$ units of $\mathrm { C } ^ { 2 } \cdot \mathrm { s } ^ { 2 } / \left( \mathrm { kg } \cdot \mathrm { m } ^ { 2 } \right)$ , that quantity could be

A) a capacitance.
B) an electric potential difference.
C) an electric field strength.
D) a dielectric constant.
E) an electric potential energy.

Question 15

Write the word or phrase that best completes each statement or answers the question.
An ideal parallel-plate capacitor has a capacitance of $C$ . If the area of the plates is doubled and the distance between the plates is halved, what is the new capacitance?

A) $2 \mathrm { C }$
B) $\mathrm { C } / 4$
C) $\mathrm { C } / 2$
D) $4 \mathrm { C }$

Question 16

Write the word or phrase that best completes each statement or answers the question.
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) $4 u$
B) $u \sqrt { 2 }$
C) $8 u$
D) $2 u$
E) $16 u$

Question 17

Write the word or phrase that best completes each statement or answers the question.
At a distance $d$ from a point charge $Q$ , the energy density in its electric field is $u$ . If we now go to a distance $d / 2$ from the charge, what is the energy density at the new location?

A) $8 u$
B) $16 u$
C) $4 u$
D) $2 u$
E) $u \sqrt { 2 }$

Question 18

Write the word or phrase that best completes each statement or answers the question.
How much work must we do on an electron to move it from point $A$ , which is at a potential of $+ 50 \mathrm {~V}$ , to point $\mathrm { B }$ , which is at a potential of $- 50 \mathrm {~V}$ , along the semicircular path shown in the figure? Assume the system is isolated from outside forces. $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $1.60 \times 10 ^ { - 17 } \mathrm {~J}$
B) $- 1.60 \times 10 ^ { - 17 } \mathrm {~J}$
C) $1.6 \mathrm {~J}$
D) $- 1.6 \mathrm {~J}$
E) This cannot be determined because we do not know the distance traveled.

Question 19

Write the word or phrase that best completes each statement or answers the question.
After a proton with an initial speed of $1.50 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$ has increased its speed by accelerating through a potential difference of $0.100 \mathrm { kV }$ , what is its final speed? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {proton } } = \right.$ $1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ )

A) $1.55 \times 10^6 \mathrm {~m} / \mathrm { s }$
B) $2.04 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$
C) $8.80 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$
D) $4.56 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$
E) $3.55 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$

Question 20

Write the word or phrase that best completes each statement or answers the question.
A proton that is initially at rest is accelerated through an electric potential difference of magnitude $500 \mathrm {~V}$ . How much kinetic energy does it gain? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $8.0 \times 10 ^ { - 17 } \mathrm {~J}$
B) $500 \mathrm {~J}$
C) $1.6 \times 10 ^ { - 19 } \mathrm {~J}$
D) $800 \mathrm {~J}$

Question 21

Write the word or phrase that best completes each statement or answers the question.
Two very small $+ 3.00 - \mu \mathrm { C }$ charges are at the ends of a meter stick. Find the electric potential (relative to infinity) at the center of the meter stick. $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $1.08 \times 10 ^ { 5 } \mathrm {~V}$
B) $2.70 \times 10 ^ { 4 } \mathrm {~V}$
C) $0.00 \mathrm {~V}$
D) $5.40 \times 10 ^ { 4 } \mathrm {~V}$

Question 22

Write the word or phrase that best completes each statement or answers the question.
Three point charges are placed at the following points in a horizontal $x - y$ plane: $+ 4.0 \mu \mathrm { C }$ is at $( 0.00 \mathrm {~m} , 0.50 \mathrm {~m} ) , + 1.0 \mu \mathrm { C }$ is at $( 0.20 \mathrm {~m} , 0.00 \mathrm {~m} )$ , and $- 5.0 \times \mu \mathrm { C }$ is at $( 0.20 \mathrm {~m} , 0.50 \mathrm {~m} )$ . Calculate the electrical potential (relative to infinity) at the origin due to these three point charges. $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Question 23

Write the word or phrase that best completes each statement or answers the question.
Point charges $+ 4.00 \mu \mathrm { C }$ and $+ 2.00 \mu \mathrm { C }$ are placed at the opposite corners of a rectangle as shown in the figure. What is the potential at point B due to these charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $\mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $89.9 \mathrm { kV }$
B) $8.99 \mathrm { kV }$
C) $11.2 \mathrm { kV }$
D) $899 \mathrm { kV }$
E) $112 \mathrm { kV }$

Question 24

Write the word or phrase that best completes each statement or answers the question.
$\mathrm { A } + 5.0 - \mu \mathrm { C }$ point charge is $12 \mathrm {~cm}$ from a $- 5.0 - \mu \mathrm { C }$ point charge. What is the magnitude of the electric field they produce at the point on the line connecting them where their electric potential (relative to infinity) is zero? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $12.5 \mathrm { MN } / \mathrm { C }$
B) $0 \mathrm {~N} / \mathrm { C }$
C) $0.75 \mathrm { MN } / \mathrm { C }$
D) $25 \mathrm { MN } / \mathrm { C }$
E) $1.5 \mathrm { MN } / \mathrm { C }$

Question 25

Write the word or phrase that best completes each statement or answers the question.
Two $3.0 \mu \mathrm { C }$ charges lie on the $x$ -axis, one at the origin and the other at $2.0 \mathrm {~m}$ . What is the potential (relative to infinity) due to these charges at a point at $6.0 \mathrm {~m}$ on the $x$ -axis? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \right.$ $\mathrm { N } \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $3400 \mathrm {~V}$
B) $11,000 \mathrm {~V}$
C) $14,000 \mathrm {~V}$
D) $9000 \mathrm {~V}$

Question 26

Write the word or phrase that best completes each statement or answers the question.
A square is $1.0 \mathrm {~m}$ on a side. Point charges of $+ 4.0 \mu \mathrm { C }$ are placed in two diagonally opposite corners. In the other two corners are placed charges of $+ 3.0 \mu \mathrm { C }$ and $- 3.0 \mu \mathrm { C }$ . What is the potential (relative to infinity) at the midpoint of the square? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $1.0 \times 10 ^ { 4 } \mathrm {~V}$
B) infinite
C) $1.0 \times 10 ^ { 6 } \mathrm {~V}$
D) $1.0 \times 10 ^ { 5 } \mathrm {~V}$
E) $0 \mathrm {~V}$

Question 27

Write the word or phrase that best completes each statement or answers the question.
How much work is needed to carry an electron from the positive terminal to the negative terminal of a $9.0 - \mathrm { V }$ battery. $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

A) $14.4 \times 10 ^ { - 19 } \mathrm {~J}$
B) $9.0 \mathrm {~J}$
C) $1.6 \times 10 ^ { - 19 } \mathrm {~J}$
D) $17 \times 10 ^ { - 19 } \mathrm {~J}$
E) $14.4 \times 10 ^ { - 19 } \mathrm {~J} / \mathrm { C }$

Question 28

Write the word or phrase that best completes each statement or answers the question.
Four point charges of magnitude $6.00 \mu \mathrm { C }$ and are at the corners of a square $2.00 \mathrm {~m}$ on each side. Two of the charges are positive, and two are negative. What is the electric potential at the center of this square, relative to infinity, due to these charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $153 \mathrm { kV }$
B) $306 \mathrm { kV }$
C) $76.4 \mathrm { kV }$
D) $0 \mathrm {~V}$
E) $61.0 \mathrm { kV }$

Question 29

Write the word or phrase that best completes each statement or answers the question.
A sphere with radius $2.0 \mathrm {~mm}$ carries a $+ 2.0 \mu \mathrm { C }$ charge. What is the potential difference, $V _ { B } - V _ { A }$ , between point $\mathrm { B }$ , which is $4.0 \mathrm {~m}$ from the center of the sphere, and point $\mathrm { A }$ , which is $6.0 \mathrm {~m}$ from the center of the sphere? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $170 \mathrm {~V}$
B) $- 1500 \mathrm {~V}$
C) $1500 \mathrm {~V}$
D) $- 0.63 \mathrm {~V}$

Question 30

Write the word or phrase that best completes each statement or answers the question.
$\mathrm { A } + 4.0 - \mu \mathrm { C }$ and a $- 4.0 - \mu \mathrm { C }$ point charge are placed as shown in the figure. What is the potential difference between points $A$ and $B$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $96 \mathrm { kV }$
B) $0 \mathrm {~V}$
C) $48 \mathrm { kV }$
D) $48 \mathrm {~V}$
E) $96 \mathrm {~V}$

Question 31

Write the word or phrase that best completes each statement or answers the question.
A $6.9 \mu \mathrm { C }$ negative point charge has a positively charged particle in an elliptical orbit about it. If the mass of the positively charged particle is $1.0 \mu \mathrm { g }$ and its distance from the point charge varies from $4.0 \mathrm {~mm}$ to $16.0 \mathrm {~mm}$ , what is the maximum potential difference through which the positive object moves? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $- 5.2 \mathrm { MV }$
B) $19 \mathrm { MV }$
C) $3.9 \mathrm { MV }$
D) $12 \mathrm { MV }$

Question 32

Write the word or phrase that best completes each statement or answers the question.
If a $\mathrm { Cu } ^ { 2 + }$ ion that is initially at rest accelerates through a potential difference of $12 \mathrm {~V}$ without friction, how much kinetic energy will it gain? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $12 \mathrm { eV }$ .
B) $3.0 \mathrm { eV }$ .
C) $6.0 \mathrm { eV }$ .
D) $24 \mathrm { eV }$ .

Question 33

Write the word or phrase that best completes each statement or answers the question.
Two $5.0 - \mu \mathrm { C }$ point charges are $12 \mathrm {~cm}$ apart. What is the electric potential (relative to infinity) of this combination at the point where the electric field due to these charges is zero? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times \right.$ $10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $0.75 \mathrm { MV }$
B) $1.5 \mathrm { MV }$
C) $12.5 \mathrm { MV }$
D) $0.0 \mathrm { MV }$
E) $25 \mathrm { MV }$

Question 34

Write the word or phrase that best completes each statement or answers the question.
If it takes $50 \mathrm {~J}$ of energy to move $10 \mathrm { C }$ of charge from point $A$ to point $B$ , what is the magnitude of the potential difference between points $A$ and $B$ ?

A) $500 \mathrm {~V}$
B) $0.50 \mathrm {~V}$
C) $50 \mathrm {~V}$
D) $5.0 \mathrm {~V}$

Question 35

Write the word or phrase that best completes each statement or answers the question.
Two $+ 6.0 - \mu \mathrm { C }$ charges are placed at two of the vertices of an equilateral triangle having sides $2.0 \mathrm {~m}$ Iong. What is the electric potential at the third vertex, relative to infinity, due to these charges? $( k =$ $1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $108 \mathrm {~V}$
B) $90 \mathrm { kV }$
C) $54 \mathrm { kV }$
D) $0 \mathrm {~V}$
E) $27 \mathrm { kV }$

Question 36

Write the word or phrase that best completes each statement or answers the question.
Two point charges of $+ 2.00 \mu \mathrm { C }$ and $+ 4.00 \mu \mathrm { C }$ are at the origin and at the point $x = 0.000 \mathrm {~m} , y =$ $- 0.300 \mathrm {~m}$ , as shown in the figure. What is the electric potential due to these charges, relative to infinity, at the point $\mathrm { P }$ at $x = 0.400 \mathrm {~m}$ on the $x$ -axis? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $117 \mathrm { kV }$
B) $36.0 \mathrm { kV }$
C) $15.7 \mathrm { kV }$
D) $56.0 \mathrm { kV }$
E) $11.7 \mathrm { kV }$

Question 37

Write the word or phrase that best completes each statement or answers the question.
The three point charges shown in the figure form an equilateral triangle with sides $4.9 \mathrm {~cm}$ long. What is the electric potential (relative to infinity) at the point indicated with the dot, which is equidistant from all three charges? Assume that the numbers in the figure are all accurate to two significant figures. $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $1900 \mathrm {~V}$
B) $1300 \mathrm {~V}$
C) $640 \mathrm {~V}$
D) $0.00 \mathrm {~V}$

Question 38

Write the word or phrase that best completes each statement or answers the question.
Three point charges, $- 2.00 \mu \mathrm { C } , + 4.00 \mu \mathrm { C }$ , and $+ 6.00 \mu \mathrm { C }$ , are located along the $x$ -axis as shown in the figure. What is the electric potential (relative to infinity) at point $\mathrm { P }$ due to these charges? $( k =$ $1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $+ 154$ kV
B) $+ 307 \mathrm { kV }$
C) $- 307 \mathrm { kV }$
D) $0.00 \mathrm { kV }$
E) $- 154 \mathrm { kV }$

Question 39

Write the word or phrase that best completes each statement or answers the question.
Point charges $+ 4.00 \mu \mathrm { C }$ and $+ 2.00 \mu \mathrm { C }$ are placed at the opposite corners of a rectangle as shown in the figure. What is the potential difference $V _ { \mathrm { A } } - V _ { \mathrm { B } }$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $+ 22.5 \mathrm { kV }$
B) $- 203 \mathrm { kV }$
C) $+ 203 \mathrm { kV }$
D) $- 22.5 \mathrm { kV }$
E) $0.00 \mathrm { kV }$

Question 40

Write the word or phrase that best completes each statement or answers the question.
A 4.0-g bead carries a charge of $20 \mu \mathrm { C }$ . The bead is accelerated from rest through a potential difference $V$ , and afterward the bead is moving at $2.0 \mathrm {~m} / \mathrm { s }$ . What is the magnitude of the potential difference $V$ ?

A) $800 \mathrm {~V}$
B) $200 \mathrm {~V}$
C) $800 \mathrm { kV }$
D) $400 \mathrm { kV }$
E) $400 \mathrm {~V}$

Question 41

Choose the one alternative that best completes the statement or answers the question.
An electric dipole with $\pm 5.0 \mu \mathrm { C }$ point charges is positioned so that the positive charge is $1.0 \mathrm {~mm}$ to the right of the origin and the negative charge is at the origin. How much work does it take to bring a $3.0 - \mu \mathrm { C }$ point charge from very far away to the point $x = 3.0 \mathrm {~mm} , y = 0.0 \mathrm {~mm}$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times \right.$ $10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $19 \mathrm {~J}$
B) $23 \mathrm {~J}$
C) $110 \mathrm {~J}$
D) $49 \mathrm {~J}$

Question 42

Choose the one alternative that best completes the statement or answers the question.
A small $4.0 - \mu C$ charge and a small $1.5 - \mu C$ charge are initially very far apart. How much work does it take to bring them to a final configuration in which the $4.0 - \mu \mathrm { C }$ charge is at the point $x = 1.0$ $\mathrm { mm } , y = 1.0 \mathrm {~mm}$ , and the $1.5 - \mu \mathrm { C }$ charge is at the point $x = 1.0 \mathrm {~mm} , y = 3.0 \mathrm {~mm}$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \right.$ $\times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $13.5 \mathrm {~kJ}$
B) $27 \mathrm {~J}$
C) $13.5 \mathrm {~J}$
D) $54 \mathrm {~J}$

Question 43

Write the word or phrase that best completes each statement or answers the question.
The potential difference between two square parallel plates is $4.00 \mathrm {~V}$ . If the plate separation is $6.00 \mathrm {~cm}$ and they each measure $1.5 \mathrm {~m}$ by $1.5 \mathrm {~m}$ , what is the magnitude of the electric field between the plates?

Question 44

Choose the one alternative that best completes the statement or answers the question.
A $7.0 - \mu \mathrm { C }$ point charge and a $9.0 - \mu \mathrm { C }$ point charge are initially extremely far apart. How much work does it take to bring the $7.0 - \mu C$ point charge to the point $x = 3.0 \mathrm {~mm} , y = 0.0 \mathrm {~mm}$ , and the $9.0 - \mu \mathrm { C }$ point charge to the point $x = - 3.0 \mathrm {~mm} , y = 0.0 \mathrm {~mm} ? \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $16 \mathrm {~J}$
B) $95 \mathrm {~J}$
C) $63 \mathrm {~J}$
D) $190 \mathrm {~J}$

Question 45

Choose the one alternative that best completes the statement or answers the question.
In a region where the electric field is uniform and points in the $+ x$ direction, the electric potential is $- 2000 \mathrm {~V}$ at $x = 8 \mathrm {~m}$ and is $+ 400 \mathrm {~V}$ at $x = 2 \mathrm {~m}$ . What is the magnitude of the electric field?

A) $200 \mathrm {~V} / \mathrm { m }$
B) $600 \mathrm {~V} / \mathrm { m }$
C) $300 \mathrm {~V} / \mathrm { m }$
D) $400 \mathrm {~V} / \mathrm { m }$
E) $500 \mathrm {~V} / \mathrm { m }$

Question 46

Choose the one alternative that best completes the statement or answers the question.
The figure shows an arrangement of two particles each having charge $Q = - 6.8 \mathrm { nC }$ and each separated by $5.0 \mathrm {~mm}$ from a proton. If the two particles are held fixed at their locations and the proton is set into motion as shown, what is the minimum speed the proton needs to totally escape from these particles? $\left( m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $\mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $8.3 \times 106 \mathrm {~m} / \mathrm { s }$
B) $1.7 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$
C) $4.3 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
D) $2.2 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$

Question 47

Write the word or phrase that best completes each statement or answers the question.
A very small $4.8 - \mathrm { g }$ particle carrying a charge of $+ 9.9 \mu \mathrm { C }$ is fired with an initial speed of $8.0 \mathrm {~m} / \mathrm { s }$ directly toward a second small $7.8 - \mathrm { g }$ particle carrying a charge of $+ 5.2 \mu \mathrm { C }$ . 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? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Question 48

Choose the one alternative that best completes the statement or answers the question.
In the figure, $+ 4.0 - \mu \mathrm { C }$ and $- 4.0 - \mu \mathrm { C }$ point charges are located as shown. Now an additional $+ 2.00 - \mu \mathrm { C }$ point charge is placed at point $\mathrm { A }$ . What is the electric potential energy of this system of three charges, relative to infinity? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $+ 26.4 \mathrm {~mJ}$
B) $- 264 \mathrm {~mJ}$
C) $+ 264 \mathrm {~mJ}$
D) $0.00 \mathrm {~J}$
E) $- 26.4 \mathrm {~mJ}$

Question 49

Write the word or phrase that best completes each statement or answers the question.
Point charges $+ 4.00 \mu \mathrm { C }$ and $+ 2.00 \mu \mathrm { C }$ are placed at the opposite corners of a rectangle as shown in the figure. If these charges are released and are free to move with no friction, what is the maximum amount of kinetic energy they will gain? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $m ^ { 2 } / C ^ { 2 }$ )

Question 50

Choose the one alternative that best completes the statement or answers the question.
An alpha particle (a helium nucleus, having charge $+ 2 e$ and mass $6.64 \times 10 ^ { - 27 } \mathrm {~kg}$ ) moves head-on at a fixed gold nucleus (having charge $+ 79 e$ ). If the distance of closest approach is $2.0 \times 10 ^ { - 10 } \mathrm {~m}$ , what was the speed of the alpha particle when it was very far away from the gold? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = \right.$ $\left. 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $2.3 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$
B) $4.6 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
C) $2.3 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$
D) $4.6 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$

Question 51

Write the word or phrase that best completes each statement or answers the question.
Two tiny particles having charges $q _ { 1 } = + 56.0 \mathrm { nC }$ and $q _ { 2 } = - 46.0 \mathrm { nC }$ are separated by $0.500 \mathrm {~m}$ and held in place, as shown in the figure. A third particle, having a charge of $54.0 \mathrm { nC }$ is placed at the point $A$ , which is $0.18 \mathrm {~m}$ to the left of $q 2$ . How much work is needed to move the third particle from point $A$ to point $B$ , which is $0.40 \mathrm {~m}$ to the left of $q 1$ . All the points in the figure lie on the same line. $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Question 52

Choose the one alternative that best completes the statement or answers the question.
Two tiny grains of sand having charges of $4.0 \mu \mathrm { C }$ and $- 4.0 \mu \mathrm { C }$ are situated along the $x$ -axis at $x _ { 1 } =$ $2.0 \mathrm {~m}$ and $x _ { 2 } = - 2.0 \mathrm {~m}$ . What is electric potential energy of these grains relative to infinity? $( k = 1 / 4$ $\pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $0 \mathrm {~J}$
B) $- 72 \mathrm {~mJ}$
C) $- 36 \mathrm {~mJ}$
D) $36 \mathrm {~mJ}$
E) $72 \mathrm {~mJ}$

Question 53

Choose the one alternative that best completes the statement or answers the question.
$\mathrm { A } + 5.0 - \mathrm { nC }$ charge is at the point $( 0.00 \mathrm {~m} , 0.00 \mathrm {~m} )$ and a $- 2.0 - \mathrm { nC }$ charge is at $( 3.0 \mathrm {~m} , 0.00 \mathrm {~m} )$ . What work is required to bring a $1.0 - \mathrm { nC }$ charge from very far away to point $( 0.00 \mathrm {~m} , 4.0 \mathrm {~m} )$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } \right.$ $= 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $11 \mathrm {~nJ}$
B) $7.7 \mathrm {~nJ}$
C) $3.6 \mathrm {~nJ}$
D) $15 \mathrm {~nJ}$

Question 54

Choose the one alternative that best completes the statement or answers the question.
The figure shows a group of three particles, all of which have charge $Q = 8.8 \mathrm { nC }$ . How much work did it take to assemble this group of charges if they all started out extremely far from each other? $( k$ $\left. = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$
$3.0 \mathrm {~cm}$

A) $5.9 \times 10 - 5 \mathrm {~J}$
B) $5.7 \times 10 ^ { - 5 } \mathrm {~J}$
C) $6.2 \times 10 ^ { - 5 } \mathrm {~J}$
D) $5.5 \times 10 - 5 \mathrm {~J}$

Question 55

Choose the one alternative that best completes the statement or answers the question.
A +3.0- $\mu \mathrm { C }$ point charge is initially extremely far from a positive point charge $Q$ . You find that it takes $41 \mathrm {~J}$ of work to bring the $+ 3.0 - \mu \mathrm { C }$ charge to the point $x = 3.0 \mathrm {~mm} , y = 0.0 \mathrm {~mm}$ and the point charge $Q$ to the point $x = - 3.0 \mathrm {~mm} , y = 0.00 \mathrm {~mm}$ . What is $Q$ ? $( k = \ldots )$

A) $4.6 \mu \mathrm { C }$
B) $55 \mathrm { nC }$
C) $27 \mathrm { pC }$
D) $9.1 \mu \mathrm { C }$

Question 56

Choose the one alternative that best completes the statement or answers the question.
How much energy is necessary to place three $+ 2.0 - \mu \mathrm { C }$ point charges at the vertices of an equilateral triangle of side $2.0 \mathrm {~cm}$ if they started out extremely far away? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \right.$ $\cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $6.7 \mathrm {~J}$
B) $5.4 \mathrm {~J}$
C) $4.5 \mathrm {~J}$
D) $7.6 \mathrm {~J}$

Question 57

Choose the one alternative that best completes the statement or answers the question.
A point charge of $+ 3.00 \mu \mathrm { C }$ and a second charge $Q$ are initially very far apart. If it takes $29.0 \mathrm {~J}$ of work to bring them to a final configuration in which the $+ 3.00 - \mu \mathrm { C }$ charge is at the point $x = 1.00$ $\mathrm { mm } , y = 1.00 \mathrm {~mm}$ , and the second charge $Q$ is at the point $x = 1.00 \mathrm {~mm} , y = 3.00 \mathrm {~mm}$ , find the magnitude of the charge $Q . \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A) $2.15 \mu \mathrm { C }$
B) $10.74 \mu \mathrm { C }$
C) $4.30 \mu \mathrm { C }$
D) $4.30 \mathrm { nC }$

Question 58

Write the word or phrase that best completes each statement or answers the question.
$\mathrm { A } + 7.5 - \mathrm { nC }$ point charge is $5.0 \mathrm {~cm}$ from a $- 9.4 - \mu \mathrm { C }$ point charge in your laboratory in California. How much work would you have to do if you left the $+ 7.5 - \mathrm { nC }$ charge in the lab but took the $- 9.4 - \mu \mathrm { C }$ charge to New York City? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Question 59

Choose the one alternative that best completes the statement or answers the question.
An electron is released from rest at a distance of $9.00 \mathrm {~cm}$ from a fixed proton. How fast will the electron be moving when it is $3.00 \mathrm {~cm}$ from the proton? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.60 \right.$ $\left. \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$

A) $4.64 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$
B) $75.0 \mathrm {~m} / \mathrm { s }$
C) $1.06 \times 10 ^ { 3 } \mathrm {~m} / \mathrm { s }$
D) $130 \mathrm {~m} / \mathrm { s }$
E) $106 \mathrm {~m} / \mathrm { s }$

Question 60

Choose the one alternative that best completes the statement or answers the question.
Two isolated copper plates, each of area $0.40 \mathrm {~m} ^ { 2 }$ , carry opposite charges of magnitude $7.08 \times 10 ^ { - 10 }$ C. They are placed opposite each other in parallel alignment, with a spacing of $4.0 \mathrm {~cm}$ between them. What is the potential difference between the plates? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

A) $3.2 \mathrm {~V}$
B) $0.40 \mathrm {~V}$
C) $7.6 \mathrm {~V}$
D) $3.0 \mathrm {~V}$
E) $8.0 \mathrm {~V}$

Question 61

Write the word or phrase that best completes each statement or answers the question.
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, $V _ { G } - V _ { D }$ , between points $G$ and D?
(b) What is the potential difference, $V$ A - $V _ { \mathrm { G } }$ , between points $\mathrm { A }$ and $\mathrm { G }$ ?

Question 62

Write the word or phrase that best completes each statement or answers the question.
Each plate of an ideal air-filled parallel-plate capacitor has an area of $0.0010 \mathrm {~m} ^ { 2 }$ , and the separation of the plates is $0.050 \mathrm {~mm}$ . An electric field of $7.4 \times 10 ^ { 6 } \mathrm {~V} / \mathrm { m }$ is present between the plates. What is the capacitance of this capacitor? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

A) $300 \mathrm { pF }$
B) $120 \mathrm { pF }$
C) $180 \mathrm { pF }$
D) $240 \mathrm { pF }$
E) $360 \mathrm { pF }$

Question 63

Write the word or phrase that best completes each statement or answers the question.
A 12.0-V battery (potential source) is connected across a $6.00 - \mu \mathrm { F }$ air-filled capacitor.
(a) How much energy can be stored this way?
(b) How much excess charge is on each plate of the capacitor?

Question 64

Write the word or phrase that best completes each statement or answers the question.
An air-filled parallel-plate capacitor is constructed with a plate area of $0.40 \mathrm {~m} ^ { 2 }$ and a plate separation of $0.10 \mathrm {~mm}$ . It is then charged to a potential difference of $12 \mathrm {~V}$ ? $\left( \varepsilon _ { 0 } = 8.85 \times \right.$ $10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 }$ )
(a) How much charge is stored on each of its plates?
(b) How much energy is stored in it?

Question 65

Write the word or phrase that best completes each statement or answers the question.
An ideal air-filled parallel-plate capacitor consists of two circular plates, each of radius $0.30 \mathrm {~mm}$ . How far apart should the plates be for the capacitance to be $300.0 - \mathrm { pF } ? \left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \right.$ $\mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 }$ )

A) $0.0042 \mu \mathrm { m }$
B) $0.0083 \mu \mathrm { m }$
C) $0.00094 \mu \mathrm { m }$
D) $0.00047 \mu \mathrm { m }$

Question 66

Write the word or phrase that best completes each statement or answers the question.
An ideal air-filled parallel-plate capacitor consists of plates that are $1.0 \mathrm {~mm}$ apart and have an area of $1.5 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ . The capacitor is connected to a $12 - \mathrm { V }$ potential source (battery). $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right.$ )
(a) What is the capacitance of this capacitor?
(b) How much charge is on each of its plates?
(c) What is the strength of the electric field between the plates?

Question 67

Write the word or phrase that best completes each statement or answers the question.
A spherical oil droplet with nine excess electrons is held stationary in an electric field between two large horizontal plates that are $2.25 \mathrm {~cm}$ apart. The field is produced by maintaining a potential difference of $0.3375 \mathrm { kV }$ across the plates, and the density of the oil is $824 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ . What is the radius of the oil drop? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

Question 68

Write the word or phrase that best completes each statement or answers the question.
The equipotential surfaces for two spherical conductors are shown in the figure, with the value of potential marked on the line for each surface.
(a) If the distance between points $A$ and $B$ is $2.5 \mathrm {~cm}$ what is the approximate intensity of the electric field between these two points?
(b) If the distance between points $C$ and $D$ is $2.5 \mathrm {~cm}$ what is the approximate intensity of the electric field between these two points?

Question 69

Write the word or phrase that best completes each statement or answers the question.
An ideal air-filled parallel plate capacitor with plate a separation of $4.0 \mathrm {~cm}$ has a plate area of $0.040$ $\mathrm { m } ^ { 2 }$ . What is the capacitance of this capacitor with air between these plates? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \right.$ $\mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 }$ )

A) $89 \mathrm { pF }$
B) $0.89 \mathrm { pF }$
C) $8.9 \mathrm { pF }$
D) $8.9 \mu \mathrm { F }$
E) $8.9 \mathrm { nF }$

Question 70

Write the word or phrase that best completes each statement or answers the question.
What charge accumulates on the plates of a $2.0 - \mu \mathrm { F }$ air-filled capacitor when it is charged until the potential difference across its plates is $100 \mathrm {~V}$ ?

A) $200 \mu \mathrm { C }$
B) $50 \mu \mathrm { C }$
C) $100 \mu \mathrm { C }$
D) $150 \mu \mathrm { C }$

Question 71

Choose the one alternative that best completes the statement or answers the question.
Two very large parallel metal plates, separated by $0.20 \mathrm {~m}$ , are connected across a $12 - \mathrm { V }$ source of potential. An electron is released from rest at a location $0.10 \mathrm {~m}$ from the negative plate. When the electron arrives at a distance $0.050 \mathrm {~m}$ from the positive plate, how much kinetic energy has the electron gained? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $9.6 \times 10 ^ { - 19 } \mathrm {~J}$
B) $4.8 \times 10 ^ { - 19 } \mathrm {~J}$
C) $7.2 \times 10 ^ { - 19 } \mathrm {~J}$
D) $2.4 \times 10 ^ { - 19 } \mathrm {~J}$

Question 72

Write the word or phrase that best completes each statement or answers the question.
Each plate of an ideal air-filled parallel-plate capacitor has an area of $0.0020 \mathrm {~m} ^ { 2 }$ , and the separation of the plates is $0.090 \mathrm {~mm}$ . An electric field of $2.1 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { C }$ is present between the plates. What is the surface charge density on the plates? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

A) $28 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$
B) $47 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$
C) $9.3 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$
D) $39 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$
E) $19 \mu \mathrm { C } / \mathrm { m } ^ { 2 }$

Question 73

Write the word or phrase that best completes each statement or answers the question.
When the potential difference between the plates of an ideal air-filled parallel plate capacitor is 35 $\mathrm { V }$ , the electric field between the plates has a strength of $750 \mathrm {~V} / \mathrm { m }$ . If the plate area is $4.0 \times 10 ^ { - 2 } \mathrm {~m} ^ { 2 }$ , what is the capacitance of this capacitor? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } 2 / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

A) $7.6 \times 10 ^ { - 10 } \mathrm {~F}$
B) $7.6 \times 10 ^ { - 11 } \mathrm {~F}$
C) $7.6 \times 10 ^ { - 12 } \mathrm {~F}$
D) $7.6 \times 10 ^ { - 14 } \mathrm {~F}$
E) None of the other choices is correct.

Question 74

Choose the one alternative that best completes the statement or answers the question.
A uniform electric field, with a magnitude of $500 \mathrm {~V} / \mathrm { m }$ , is points in the $+ x$ direction. If the potential at $x = 5.0 \mathrm {~m}$ is $2500 \mathrm {~V}$ , what is the potential at $x = 2.0 \mathrm {~m}$ ?

A) $2.0 \mathrm { kV }$
B) $0.50 \mathrm { kV }$
C) $5.0 \mathrm { kV }$
D) $1.0 \mathrm { kV }$
E) $4.0 \mathrm { kV }$

Question 75

Write the word or phrase that best completes each statement or answers the question.
An ideal air-filled parallel-plate capacitor with horizontal plates has a plate separation of $5.0 \mathrm {~cm}$ . If the potential difference between the plates is $2000 \mathrm {~V}$ , with the top plate at the higher potential, what are the magnitude and direction of the electric field between the plates?

A) $40000 \mathrm {~N} / \mathrm { C }$ downward
B) $40000 \mathrm {~N} / \mathrm { C }$ upward
C) $100 \mathrm {~N} / \mathrm { C }$ upward
D) $100 \mathrm {~N} / \mathrm { C }$ downward

Question 76

Choose the one alternative that best completes the statement or answers the question.
A space probe approaches a planet, taking measurements as it goes. If it detects a potential difference of $6000 \mathrm { MV }$ between the altitudes of $253,000 \mathrm {~km}$ and $276,000 \mathrm {~km}$ above the planet's surface, what is the approximate electric field strength produced by the planet at $264,500 \mathrm {~km}$ above the surface? Assume the electric field strength is approximately constant at these altitudes.

A) $493 \mu \mathrm { N } / \mathrm { C }$
B) $0.261 \mathrm {~N} / \mathrm { C }$
C) $561 \mathrm {~N} / \mathrm { C }$
D) $261 \mathrm {~N} / \mathrm { C }$

Question 77

Write the word or phrase that best completes each statement or answers the question.
A 3.0-pFcapacitor consists of two large closely-spaced parallel plates that have surface charge densities of $\pm 1.0 \mathrm { nC } / \mathrm { mm } ^ { 2 }$ . If the potential across the plates is $23.0 \mathrm { kV }$ with only air between them, find the surface area of each of the plates. $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right.$ )

A) $35 \mathrm {~mm} ^ { 2 }$
B) $69 \mathrm {~mm} ^ { 2 }$
C) $0.0072 \mathrm {~mm} ^ { 2 }$
D) $0.014 \mathrm {~mm} ^ { 2 }$

Question 78

Choose the one alternative that best completes the statement or answers the question.
A proton moves $0.10 \mathrm {~m}$ along the direction of an electric field of magnitude $3.0 \mathrm {~V} / \mathrm { m }$ . What is the change in kinetic energy of the proton? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $3.2 \times 10 ^ { - 20 } \mathrm {~J}$
B) $1.6 \times 10 ^ { - 20 } \mathrm {~J}$
C) $8.0 \times 10 ^ { - 21 } \mathrm {~J}$
D) $4.8 \times 10 ^ { - 20 } \mathrm {~J}$

Question 79

Choose the one alternative that best completes the statement or answers the question.
A battery maintains the electrical potential difference of $6.0 - \mathrm { V }$ between two large parallel metal plates separated by $1.0 \mathrm {~mm}$ . What is the strength of the electric field between the plates?

A) $6.0 \mathrm {~V} / \mathrm { m }$
B) zero
C) $600 \mathrm {~V} / \mathrm { m }$
D) $6000 \mathrm {~V} / \mathrm { m }$

Question 80

Write the word or phrase that best completes each statement or answers the question.
Two large parallel plates are separated by $1.0 \mathrm {~mm}$ of air. If the potential difference between them is $3.0 \mathrm {~V}$ , what is the magnitude of their surface charge densities? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

A) $2.7 \times 10 ^ { - 8 } \mathrm { C } / \mathrm { m } ^ { 2 }$
B) $3.3 \times 10 ^ { - 4 } \mathrm { C } / \mathrm { m } ^ { 2 }$
C) $1.6 \times 10 ^ { - 4 } \mathrm { C } / \mathrm { m } ^ { 2 }$
D) $5.3 \times 10 ^ { - 8 } \mathrm { C } / \mathrm { m } ^ { 2 }$