Deck 17: Electric Potential

Question 1

The potential energy of a $3.5 \mathrm{pC}$ charge separated by $6.2 \mathrm{~cm}$ from a $1.6 \mu \mathrm{C}$ charge is

A) $1.2 \times 10^{-5} \mathrm{~J}$ .
B) $8.1 \times 10^{-5} \mathrm{~J}$ .
C) $8.1 \times 10^{-7} \mathrm{~J}$ .
D) $1.0 \times 10^{-5} \mathrm{~J}$ .
E) $1.3 \times 10^{-7} \mathrm{~J}$ .

Answer 1

$8.1 \times 10^{-7} \mathrm{~J}$ .

Question 2

What is the distance between a $-2.00 \mu \mathrm{C}$ charge and a $-3.00 \mu \mathrm{C}$ charge if their potential energy is $0.491 \mathrm{~J}$ ?

A) $25.0 \mathrm{~cm}$
B) $11.0 \mathrm{~cm}$
C) $3.14 \mathrm{~cm}$
D) $15.5 \mathrm{~cm}$
E) $0.911 \mathrm{~cm}$

Answer 2

$11.0 \mathrm{~cm}$

Question 3

The SI unit for electric potential energy is equivalent to

A) $C \cdot m^{2}$ .
B) $\mathrm{N} \cdot \mathrm{m}^{2}$ .
C) $\mathrm{N} / \mathrm{m}$ .
D) $\mathrm{V} \cdot \mathrm{C}$ .
E) none of these choices are correct

Answer 3

$\mathrm{V} \cdot \mathrm{C}$ .

Question 4

Three point charges, $\mathrm{q}_{1}, \mathrm{q}_{2}$ , and $\mathrm{q}_{3}$ , are arranged so the potential energy for the pair $\mathrm{q}_{1}$ and $\mathrm{q}_{2}$ is $0.12 \mathrm{~J}$ and for the pair $\mathrm{q}_{2}$ and $\mathrm{q}_{3}$ is $0.23 \mathrm{~J}$ . What is the potential energy for the pair $\mathrm{q}_{1}$ and $\mathrm{q}_{3}$ ?

A) $-0.35 \mathrm{~J}$
B) $0.35 \mathrm{~J}$
C) $0.11 \mathrm{~J}$
D) $-0.11 \mathrm{~J}$
E) Insufficient information is given for a unique answer

Question 5

Three point charges, $q_{1}, q_{2}$ , and $q_{3}$ , are arranged so the potential energy for the pair $q_{1}$ and $q_{2}$ is $0.12 \mathrm{~J}$ and for the pair $\mathrm{q}_{2}$ and $\mathrm{q}_{3}$ is $0.23 \mathrm{~J}$ . If the total potential energy of the arrangement is $0.60 \mathrm{~J}$ , what is the potential energy of the pair $\mathrm{q}_{1}$ and $\mathrm{q}_{3}$ ?

A) $0.95 \mathrm{~J}$
B) $0.11 \mathrm{~J}$
C) $0.25 \mathrm{~J}$
D) $0.35 \mathrm{~J}$
E) Insufficient information is given for a unique answer

Question 6

Three point charges, $\mathrm{q}_{1}=2.0 \mu \mathrm{C}, \mathrm{q}_{2}=2.0 \mu \mathrm{C}$ , and $\mathrm{q}_{3}=-1.0 \mu \mathrm{C}$ , are located at the vertices of an equilateral triangle of side length $30 \mathrm{~cm}$ . What is the potential energy of this arrangement?

A) $-0.12 \mathrm{~J}$
B) 0
C) $-0.24 \mathrm{~J}$
D) $0.12 \mathrm{~J}$
E) $0.24 \mathrm{~J}$

Question 7

Three point charges, $q_{1}, q_{2}$ , and $q_{3}$ , are located at the vertices of an equilateral triangle. If $q_{1}=q_{2}$ , what value must $\mathrm{q}_{3}$ have so that the total potential energy of the arrangement is zero?

A) $\left(\mathrm{q}_{1}+\mathrm{q}_{2}\right) / 2$
B) $-0.5 \mathrm{q}_{1}$
C) $\mathrm{q}_{1}$
D) $0.5 \mathrm{q}_{1}$
E) no value will have this result

Question 8

The unit of electric potential, the volt, is equal to a

A) $\mathrm{C} \cdot \mathrm{N}$ .
B) $\mathrm{J} 2 / \mathrm{C}$ .
C) $\mathrm{J} / \mathrm{C} 2$ .
D) $\mathrm{J} / \mathrm{C}$ .
E) $\mathrm{C}^{2} \cdot \mathrm{N} / \mathrm{s}$ .

Question 9

A $2.5-\mathrm{mC}$ charge is on the $y$ -axis at $y=3.0 \mathrm{~m}$ , and a $6.3-\mathrm{mC}$ charge is on the $x$ -axis at $x=3.0 \mathrm{~m}$ . What is the direction of the electric potential at the origin?

A) $168^{\circ}$
B) $332^{\circ}$
C) $292^{\circ}$
D) $22.0^{\circ}$
E) potential has no direction

Question 10

What is the potential at a distance of $0.0529 \mathrm{~nm}$ from a proton?

A) $9.11 \mathrm{pC}$
B) $-27.2 \mathrm{~V}$
C) $27.2 \mathrm{~V}$
D) $13.6 \mathrm{~V}$
E) $-13.6 \mathrm{~V}$

Question 11

A charge $q_{1}$ is placed on the $y$ -axis at $y=4.0 \mathrm{~m}$ and the resulting potential at the position $(3.0 \mathrm{~m}, 4.0 \mathrm{~m})$ is $3.0 \mathrm{~V}$ . The charge $\mathrm{q}_{1}$ is removed and a charge $\mathrm{q}_{2}$ is placed on the $\mathrm{x}$ -axis at $\mathrm{x}=3.0 \mathrm{~m}$ and the resulting potential at the position $(3.0 \mathrm{~m}, 4.0 \mathrm{~m})$ is $4.0 \mathrm{~V}$ . If both charges are in place simultaneously, what is the potential at $(3.0 \mathrm{~m}, 4.0 \mathrm{~m})$ ?

A) $12 \mathrm{~V}$
B) $7.0 \mathrm{~V}$
C) $3.5 \mathrm{~V}$
D) $1.0 \mathrm{~V}$
E) $5.0 \mathrm{~V}$

Question 12

A $2.00 \mathrm{nC}$ charge is placed on the $\mathrm{x}$ -axis at $\mathrm{x}=-3.00 \mathrm{~cm}$ , another $2.00 \mathrm{nC}$ charge is placed on the $\mathrm{x}$ -axis at $\mathrm{x}=3.00 \mathrm{~cm}$ , and a third $2.00 \mathrm{nC}$ charge is placed on the $\mathrm{y}$ -axis at $\mathrm{y}=3.00 \mathrm{~cm}$ . What is the potential at the origin?

A) $3600 \mathrm{~V}$
B) $108 \mathrm{~V}$
C) $5400 \mathrm{~V}$
D) $2700 \mathrm{~V}$
E) $1800 \mathrm{~V}$

Question 13

A conducting sphere of radius $20 \mathrm{~cm}$ is charged to a potential of $1.0 \times 106$ volts. What is the charge on its surface?

A) $4.7 \mathrm{mC}$
B) $22 \mu \mathrm{C}$
C) $9.0 \mathrm{nC}$
D) $16 \mathrm{mC}$
E) $4.4 \mu \mathrm{C}$

Question 14

A conducting sphere of radius $20 \mathrm{~cm}$ is charged so that the electric field reaches $3.0 \times 10^{5} \mathrm{~V} / \mathrm{m}$ at its surface. What is the potential at the surface of the sphere?

A) $6.0 \times 104 \mathrm{~V}$
B) $1.5 \times 10^{4} \mathrm{~V}$
C) $2.7 \times 10^{5} \mathrm{~V}$
D) $3.0 \times 10^{4} \mathrm{~V}$
E) $4.5 \times 10^{4} \mathrm{~V}$

Question 15

How much charge is on a conducting sphere of diameter $20 \mu \mathrm{m}$ if its surface potential is $50 \mathrm{mV}$ ?

A) $56 \times 10^{-18} \mathrm{C}$
B) $50 \times 10^{-19} \mathrm{C}$
C) $1.6 \times 10^{-19} \mathrm{C}$
D) $32 \times 10^{-16} \mathrm{C}$
E) $14 \times 10^{-17} \mathrm{C}$

Question 16

If protons are accelerated from rest in a Van de Graff accelerator through a potential difference of $1.00 \mathrm{MV}$ , what is their resulting speed?

A) $3.67 \times 10^{8} \mathrm{~m} / \mathrm{s}$
B) $6.92 \times 10^{6} \mathrm{~m} / \mathrm{s}$
C) $6.25 \times 10^{7} \mathrm{~m} / \mathrm{s}$
D) $1.38 \times 10^{7} \mathrm{~m} / \mathrm{s}$
E) $9.79 \times 10^{6} \mathrm{~m} / \mathrm{s}$

Question 17

A helium nucleus is accelerated from rest through a potential difference $\mathrm{V}$ to a kinetic energy of $3.2 \times 10^{-13} \mathrm{~J}$ . What is $\mathrm{V}$ ?

A) $2.0 \mathrm{MV}$
B) $1.6 \mathrm{MV}$
C) $1.0 \mathrm{MV}$
D) $0.51 \mathrm{MV}$
E) $3.2 \mathrm{MV}$

Question 18

An air-filled parallel plate capacitor has plates of area $100 \mathrm{~cm}^{2}$ and separation $0.25 \mathrm{~mm}$ . What is its capacitance?

A) $88 \mu \mathrm{F}$
B) $40 \mathrm{nF}$
C) $88 \mathrm{pF}$
D) $4.4 \mu \mathrm{F}$
E) $0.35 \mathrm{nF}$

Question 19

A parallel plate capacitor has a paper dielectric having dielectric strength $8.0 \mathrm{kV} / \mathrm{mm}$ and dielectric constant 3.0. The plate area is $3000 \mathrm{~cm}^{2}$ and the plate separation is $0.50 \mathrm{~mm}$ . What is the capacitance?

A) $4.2 \mathrm{nF}$
B) $5.3 \mathrm{nF}$
C) $4.2 \mathrm{pF}$
D) $1.6 \mathrm{nF}$
E) $16 \mathrm{nF}$

Question 20

If a $0.20 \mathrm{pF}$ capacitor has a voltage of $40 \mathrm{mV}$ , how many more electrons are on the negative plate than on the positive plate?

A) $5.0 \times 104$
B) $8.0 \times 1014$
C) $4.0 \times 10^{3}$
D) $1.0 \times 10^{5}$
E) none, the electrons are in equal numbers on the plates

Question 21

The unit $\mathrm{F}$ , the farad, is equal to which of the following?

A) $\mathrm{C} / \mathrm{V}$
B) $\mathrm{V} / \mathrm{m}$
C) $\mathrm{V} 2 / \mathrm{C}$
D) $\mathrm{C} / \mathrm{V} 2$
E) $\mathrm{V} / \mathrm{C}$

Question 22

A parallel plate capacitor has a paper dielectric having dielectric strength $8.00 \mathrm{kV} / \mathrm{mm}$ and dielectric constant 3.00. The plate area is $3000 \mathrm{~cm}^{2}$ and the plate separation is $0.500 \mathrm{~mm}$ . If $10.0 \mathrm{~V}$ are applied to this capacitor, what is the charge on the capacitor?

A) $16.0 \mathrm{nC}$
B) $42.0 \mu \mathrm{C}$
C) $50.0 \mu \mathrm{C}$
D) $42.0 \mathrm{nC}$
E) $159 \mathrm{nC}$

Question 23

What area plates would a $1.0 \mathrm{~F}$ parallel plate capacitor have, with a plate separation of $0.10 \mathrm{~mm}$ and a dielectric of constant 10 ?

A) $5500 \mathrm{~cm}^{2}$
B) $130 \mathrm{~m}^{2}$
C) $1.1 \times 106 \mathrm{~m}^{2}$
D) $1000 \mathrm{~cm}^{2}$
E) $4.4 \times 10^{9} \mathrm{~m}^{2}$

Question 24

A parallel plate capacitor has a paper dielectric having dielectric strength $8.0 \mathrm{kV} / \mathrm{mm}$ and dielectric constant 3.0. The plate area is $3000 \mathrm{~cm}^{2}$ and the plate separation is $0.50 \mathrm{~mm}$ . What is the highest voltage that can be applied to this capacitor before breakdown occurs?

A) $4.0 \times 10^{3} \mathrm{~V}$
B) $1.2 \times 10^{4} \mathrm{~V}$
C) $15 \mathrm{~V}$
D) $4.0 \times 10^{2} \mathrm{~V}$
E) $1.2 \times 10^{2} \mathrm{~V}$

Question 25

The electric field in the dielectric-filled region between the plates of a capacitor is E. What is the charge density on the plates?

A) $\kappa \varepsilon_{0} \mathrm{E}$
B) $\mathrm{E} \cdot \mathrm{V}$
C) $\mathrm{E}^{2} \varepsilon_{0}$
D) $\mathrm{V}^{2} \cdot \mathrm{E}$
E) $\varepsilon_{0} \mathrm{E}$

Question 26

The electric potential at a distance $d$ from a point charge is $\mathrm{V}$ . At a distance $\mathrm{d}$ ', the potential is $2 \mathrm{~V}$ . What is the ratio of electric field at $\mathrm{d}$ to that at $\mathrm{d}$ ?

A) more information is necessary
B) $1 / 4$
C) 2
D) 4
E) $1 / 2$

Question 27

A pair of parallel conducting plates have potentials of $-17 \mathrm{~V}$ and $55 \mathrm{~V}$ , respectively. An electron is ejected from the plate at potential $-17 \mathrm{~V}$ and travels to the plate at $55 \mathrm{~V}$ . What is the speed of the electron as it strikes the $55 \mathrm{~V}$ plate, assuming it left the $-17 \mathrm{~V}$ plate starting from rest? The mass of the electron is $9.11 \times$ $10^{-31} \mathrm{~kg}$ .

A) $3.6 \times 10^{6} \mathrm{~m} / \mathrm{s}$
B) $2.2 \times 10^{6} \mathrm{~m} / \mathrm{s}$ .
C) $3.1 \times 10^{6} \mathrm{~m} / \mathrm{s}$
D) $5.0 \times 10^{6}\mathrm{~m} / \mathrm{s}$

Question 28

The electron is projected horizontally with a speed of $5.0 \times 10^{6} \mathrm{~m}$ exactly in the middle of two parallel plates at potentials of $-40 \mathrm{~V}$ and $104 \mathrm{~V}$ , respectively. The plate separation is $3.0 \mathrm{~cm}$ . The plates are long enough that the electron, rather than passing completely between the plates, eventually strikes the plate sitting at $104 \mathrm{~V}$ potential. What is the speed of the electron when it strikes the plate? The mass of the electron is $9.11 \times 10^{-31} \mathrm{~kg}$ .

A) $6.0 \times 106 \mathrm{~m} / \mathrm{s}$
B) $7.1 \times 106 \mathrm{~m} / \mathrm{s}$
C) $8.7 \times 106 \mathrm{~m} / \mathrm{s}$
D) $5.0 \times 10^{6} \mathrm{~m} / \mathrm{s}$

Question 29

Which of the following statements is true?

A) If the electric field is zero at a point, then the electric potential is zero at that point also.
B) The electric field is large where the potential is large, and vice versa.
C) If the electric potential is zero at a point, then the electric field is zero at that point also.
D) If the electric potential is zero throughout a region of space, then the electric field is necessarily also zero there.
E) If the electric field is zero throughout a region of space, then the electric potential is necessarily also zero there.

Question 30

The capacitance of a parallel plate capacitor changes when a dielectric is inserted between the plates. This is mainly due to

A) the polarizability of the material, which sets up an electric field opposite to the applied field, thus reducing the electric field strength in the region.
B) the fact that dielectrics have excess charge that then "shields" the plates from each other, reducing the electric field in the region.
C) the existence of denser matter than air or vacuum, which forms a barrier for electric field lines and reduces the electric field in the region.
D) None of these.