Question 1

Equipotentials are lines along which

Accepted Answer

A) the electric field is constant in magnitude and direction. 
B) the electric charge is constant in magnitude and direction. 
C) maximum work against electrical forces is required to move a charge at constant speed. 
D) a charge may be moved at constant speed without work against electrical forces. 
E) charges move by themselves. 
A) the electric field is constant in magnitude and direction. 
B) the electric charge is constant in magnitude and direction. 
C) maximum work against electrical forces is required to move a charge at constant speed. 
D) a charge may be moved at constant speed without work against electrical forces. 
E) charges move by themselves.

Question 2

A charge of 10 nC is distributed uniformly along the x axis from x = -2 m to x = +3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point x = +5 m on the x axis?

Accepted Answer

A)  $\int _ { - 2 } ^ { 3 } \frac { 90 d x } { x }$ 
B)  $\int _ { - 2 } ^ { 3 } \frac { 90 d x } { 5 - x }$ 
C)  $\int _ { - 2 } ^ { 3 } \frac { 18 d x } { x }$ 
D)  $\int _ { - 2 } ^ { 3 } \frac { 18 d x } { 5 - x }$ 
E)  $\int _ { - 2 } ^ { 3 } \frac { 90 d x } { 5 + x }$ 
A)  $\int _ { - 2 } ^ { 3 } \frac { 90 d x } { x }$ 
B)  $\int _ { - 2 } ^ { 3 } \frac { 90 d x } { 5 - x }$ 
C)  $\int _ { - 2 } ^ { 3 } \frac { 18 d x } { x }$ 
D)  $\int _ { - 2 } ^ { 3 } \frac { 18 d x } { 5 - x }$ 
E)  $\int _ { - 2 } ^ { 3 } \frac { 90 d x } { 5 + x }$

Question 3

A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them.When it is connected to a battery of voltage V0,it has charge of magnitude Q0 on its plates.The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery.After the plates are 2d apart,the capacitance of the capacitor and the magnitude of the charge on the plates are

Accepted Answer

A)  $\frac { 1 } { 2 }$ C0, $\frac { 1 } { 2 }$ Q0 
B)  $\frac { 1 } { 2 }$ C0,Q0 
C) C0,Q0 
D) 2C0,Q0 
E) 2C0,2Q0 
A)  $\frac { 1 } { 2 }$ C0, $\frac { 1 } { 2 }$ Q0 
B)  $\frac { 1 } { 2 }$ C0,Q0 
C) C0,Q0 
D) 2C0,Q0 
E) 2C0,2Q0

Question 4

A series of 3 uncharged concentric spherical conducting shells surround a small central charge q.The potential at a point outside the third shell,at distance r from the center,and relative to V = 0 at $\infty$,is

Accepted Answer

A)  $- \frac { 3 k _ { e } q } { r }$ . 
B)  $- \frac { ( \ln 3 ) k _ { e } q } { r }$ . 
C)  $+ \frac { k _ { e } q } { r }$ . 
D)  $+ \frac { ( \ln 3 ) k _ { e } q } { r }$ . 
E)  $+ \frac { 3 k _ { e } q } { r }$ . 
A)  $- \frac { 3 k _ { e } q } { r }$ . 
B)  $- \frac { ( \ln 3 ) k _ { e } q } { r }$ . 
C)  $+ \frac { k _ { e } q } { r }$ . 
D)  $+ \frac { ( \ln 3 ) k _ { e } q } { r }$ . 
E)  $+ \frac { 3 k _ { e } q } { r }$ .

Question 5

To recharge a 12-V battery,a battery charger must move 3.6 * 105 C of charge from the negative to the positive terminal.What amount of work is done by the battery charger? How many kilowatt hours is this?

Accepted Answer

The answer of To recharge a 12-V battery,a battery charger...

Question 6

A 0.16 pF parallel-plate capacitor is charged to 10 V.Then the battery is disconnected from the capacitor.When 1.00 *107 electrons are now placed on the negative plate of the capacitor,the voltage between the plates changes by

Accepted Answer

A) -5.0 V. 
B) -1.1 V. 
C) 0 V. 
D) +1.1 V. 
E) +5.0 V. 
A) -5.0 V. 
B) -1.1 V. 
C) 0 V. 
D) +1.1 V. 
E) +5.0 V.

Question 7

Which of the following materials has the highest dielectric constant?

Accepted Answer

A) air 
B) Mylar 
C) paper 
D) Pyrex glass 
E) water 
A) air 
B) Mylar 
C) paper 
D) Pyrex glass 
E) water

Question 8

Regarding the Earth and a cloud layer 800 m above the Earth as the "plates" of a capacitor,calculate the capacitance if the cloud layer has an area of 1.0 km2.If an electric field of 2.0 * 106 N/C makes the air break down and conduct electricity (lightning),what is the maximum charge the cloud can hold?

Accepted Answer

The answer of Regarding the Earth and a cloud layer...

Question 9

When a positive charge is released and moves along an electric field line,it moves to a position of

Accepted Answer

A) lower potential and lower potential energy. 
B) lower potential and higher potential energy. 
C) higher potential and lower potential energy. 
D) higher potential and higher potential energy. 
E) greater magnitude of the electric field. 
A) lower potential and lower potential energy. 
B) lower potential and higher potential energy. 
C) higher potential and lower potential energy. 
D) higher potential and higher potential energy. 
E) greater magnitude of the electric field.

Question 10

Into the gap between the plates of a parallel plate capacitor of capacitance $C _ { 0 }$ a slab of metal is inserted halfway between the plates filling one fourth of the gap between the plates.What is the resulting new capacitance?

Accepted Answer

A)  $\frac { 3 } { 4 } C _ { 0 }$ 
B)  $\frac { 4 } { 3 } C _ { 0 }$ 
C)  $\frac { 9 } { 16 } C _ { 0 }$ 
D)  $\frac { 16 } { 9 } C _ { 0 }$ 
E)  $\frac { 5 } { 4 } C _ { 0 }$ 
A)  $\frac { 3 } { 4 } C _ { 0 }$ 
B)  $\frac { 4 } { 3 } C _ { 0 }$ 
C)  $\frac { 9 } { 16 } C _ { 0 }$ 
D)  $\frac { 16 } { 9 } C _ { 0 }$ 
E)  $\frac { 5 } { 4 } C _ { 0 }$

Question 11

A system consisting of a negatively-charged particle and an electric field

Accepted Answer

A) gains potential difference and kinetic energy when the charged particle moves in the direction of the field. 
B) loses electric potential energy when the charged particle moves in the direction of the field. 
C) gains kinetic energy when the charged particle moves in the direction of the field. 
D) gains electric potential energy when the charged particle moves in the direction of the field. 
E) gains potential difference and electric potential energy when the charged particle moves in the direction of the field. 
A) gains potential difference and kinetic energy when the charged particle moves in the direction of the field. 
B) loses electric potential energy when the charged particle moves in the direction of the field. 
C) gains kinetic energy when the charged particle moves in the direction of the field. 
D) gains electric potential energy when the charged particle moves in the direction of the field. 
E) gains potential difference and electric potential energy when the charged particle moves in the direction of the field.

Question 12

The electric field in the region defined by the y-z plane and the negative x axis is given by E = -ax,where a is a constant.(There is no field for positive values of x. )As -x increases in magnitude,relative to V = 0 at the origin,the electric potential in the region defined above is

Accepted Answer

A) a decreasing function proportional to -|x2|. 
B) a decreasing function proportional to -|x|. 
C) constant. 
D) an increasing function proportional to +|x|. 
E) an increasing function proportional to +|x2|. 
A) a decreasing function proportional to -|x2|. 
B) a decreasing function proportional to -|x|. 
C) constant. 
D) an increasing function proportional to +|x|. 
E) an increasing function proportional to +|x2|.

Question 13

Charge of uniform linear density 6.0 nC/m is distributed along the x axis from x = 0 to x = +3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point y = +4 m on the y axis?

Accepted Answer

A)  $\int _ { 0 } ^ { 3 } \frac { 54 d x } { \left( x ^ { 2 } + 16 \right) ^ { 1 / 2 } }$ 
B)  $\int _ { 0 } ^ { 3 } \frac { 18 d x } { \left( x ^ { 2 } + 16 \right) ^ { 1 / 2 } }$ 
C)  $\int _ { 0 } ^ { 3 } \frac { 54 d x } { x ^ { 2 } + 16 }$ 
D)  $\int _ { 0 } ^ { 3 } \frac { 18 d x } { x ^ { 2 } + 16 }$ 
E)  $\int _ { 0 } ^ { 3 } \frac { 108 d x } { \left( x ^ { 2 } + 16 \right) ^ { 1 / 2 } }$ 
A)  $\int _ { 0 } ^ { 3 } \frac { 54 d x } { \left( x ^ { 2 } + 16 \right) ^ { 1 / 2 } }$ 
B)  $\int _ { 0 } ^ { 3 } \frac { 18 d x } { \left( x ^ { 2 } + 16 \right) ^ { 1 / 2 } }$ 
C)  $\int _ { 0 } ^ { 3 } \frac { 54 d x } { x ^ { 2 } + 16 }$ 
D)  $\int _ { 0 } ^ { 3 } \frac { 18 d x } { x ^ { 2 } + 16 }$ 
E)  $\int _ { 0 } ^ { 3 } \frac { 108 d x } { \left( x ^ { 2 } + 16 \right) ^ { 1 / 2 } }$

Question 14

A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them.When it is connected to a battery of voltage V0,it has charge of magnitude Q0 on its plates.While it is connected to the battery,the space between the plates is filled with a material of dielectric constant 3.After the dielectric is added,the magnitude of the charge on the plates and the new capacitance are

Accepted Answer

A)  $\frac { 1 } { 3 }$ Q0, $\frac { 1 } { 3 }$ C0 
B) Q0, $\frac { 1 } { 3 }$ C0 
C) Q0,C0 
D) 3Q0,C0 
E) 3Q0,3C0 
A)  $\frac { 1 } { 3 }$ Q0, $\frac { 1 } { 3 }$ C0 
B) Q0, $\frac { 1 } { 3 }$ C0 
C) Q0,C0 
D) 3Q0,C0 
E) 3Q0,3C0

Question 15

A particle (charge 7.5 $\mu$C)is released from rest at a point on the x axis,x = 10 cm.It begins to move due to the presence of a 2.0-$\mu$C charge which remains fixed at the origin.What is the kinetic energy of the particle at the instant it passes the point x = 1.0 m?

Accepted Answer

A) 3.0 J 
B) 1.8 J 
C) 2.4 J 
D) 1.2 J 
E) 1.4 J 
A) 3.0 J 
B) 1.8 J 
C) 2.4 J 
D) 1.2 J 
E) 1.4 J

Question 16

The electric field in a region of space is given by Ex = (3.0x)N/C,Ey = Ez = 0,where x is in m.Points A and B are on the x axis at xA = 3.0 m and xB = 5.0 m.Determine the potential difference VB - VA.

Accepted Answer

A) -24 V 
B) +24 V 
C) -18 V 
D) +30 V 
E) -6.0 V 
A) -24 V 
B) +24 V 
C) -18 V 
D) +30 V 
E) -6.0 V

Question 17

A 20-$\mu$F capacitor charged to 2.0 kV and a 40-$\mu$F capacitor charged to 3.0 kV are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final charge on the 20-$\mu$F capacitor after the two are so connected?

Accepted Answer

A) 53 mC 
B) 27 mC 
C) 40 mC 
D) 80 mC 
E) 39 mC 
A) 53 mC 
B) 27 mC 
C) 40 mC 
D) 80 mC 
E) 39 mC

Question 18

What is the total energy stored by C3 when C1 = 50 $\mu$F,C2 = 30 $\mu$F,C3 = 36 $\mu$F,C4 = 12 $\mu$F,and V0 = 30 V?

Accepted Answer

A) 6.3 mJ 
B) 25 mJ 
C) 57 mJ 
D) 1.6 mJ 
E) 14 mJ 
A) 6.3 mJ 
B) 25 mJ 
C) 57 mJ 
D) 1.6 mJ 
E) 14 mJ

Question 19

Three charged particles are positioned in the xy plane: a 50-nC charge at y = 6 m on the y axis,a -80-nC charge at x = -4 m on the x axis,and a 70-nc charge at y = -6 m on the y axis.What is the electric potential (relative to a zero at infinity)at the point x = 8 m on the x axis?

Accepted Answer

A) +81 V 
B) +48 V 
C) +5.8 V 
D) -72 V 
E) -18 V 
A) +81 V 
B) +48 V 
C) +5.8 V 
D) -72 V 
E) -18 V

Question 20

A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them.When it is connected to a battery of voltage V0,it has charge of magnitude Q0 on its plates.The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery.After the plates are 2d apart,the magnitude of the charge on the plates and the potential difference between them are

Accepted Answer

A)  $\frac { 1 } { 2 }$ Q0, $\frac { 1 } { 2 }$ V0 
B)  $\frac { 1 } { 2 }$ Q0,V0 
C) Q0,V0 
D) 2Q0,V0 
E) 2Q0,2V0 
A)  $\frac { 1 } { 2 }$ Q0, $\frac { 1 } { 2 }$ V0 
B)  $\frac { 1 } { 2 }$ Q0,V0 
C) Q0,V0 
D) 2Q0,V0 
E) 2Q0,2V0

Exam 20: Electric Potential and Capacitance

Equipotentials are lines along which

A charge of 10 nC is distributed uniformly along the x axis from x = -2 m to x = +3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point x = +5 m on the x axis?

A series of 3 uncharged concentric spherical conducting shells surround a small central charge q.The potential at a point outside the third shell,at distance r from the center,and relative to V = 0 at ∞\infty∞ ,is

To recharge a 12-V battery,a battery charger must move 3.6 * 105 C of charge from the negative to the positive terminal.What amount of work is done by the battery charger? How many kilowatt hours is this?

A 0.16 pF parallel-plate capacitor is charged to 10 V.Then the battery is disconnected from the capacitor.When 1.00 *107 electrons are now placed on the negative plate of the capacitor,the voltage between the plates changes by

Which of the following materials has the highest dielectric constant?

When a positive charge is released and moves along an electric field line,it moves to a position of

Into the gap between the plates of a parallel plate capacitor of capacitance C0C _ { 0 }C0​ a slab of metal is inserted halfway between the plates filling one fourth of the gap between the plates.What is the resulting new capacitance?

A system consisting of a negatively-charged particle and an electric field

The electric field in the region defined by the y-z plane and the negative x axis is given by E = -ax,where a is a constant.(There is no field for positive values of x. )As -x increases in magnitude,relative to V = 0 at the origin,the electric potential in the region defined above is

Charge of uniform linear density 6.0 nC/m is distributed along the x axis from x = 0 to x = +3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point y = +4 m on the y axis?

A particle (charge 7.5 μ\muμ C)is released from rest at a point on the x axis,x = 10 cm.It begins to move due to the presence of a 2.0- μ\muμ C charge which remains fixed at the origin.What is the kinetic energy of the particle at the instant it passes the point x = 1.0 m?

The electric field in a region of space is given by Ex = (3.0x)N/C,Ey = Ez = 0,where x is in m.Points A and B are on the x axis at xA = 3.0 m and xB = 5.0 m.Determine the potential difference VB - VA.

A 20- μ\muμ F capacitor charged to 2.0 kV and a 40- μ\muμ F capacitor charged to 3.0 kV are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final charge on the 20- μ\muμ F capacitor after the two are so connected?

What is the total energy stored by C3 when C1 = 50 μ\muμ F,C2 = 30 μ\muμ F,C3 = 36 μ\muμ F,C4 = 12 μ\muμ F,and V0 = 30 V?

Three charged particles are positioned in the xy plane: a 50-nC charge at y = 6 m on the y axis,a -80-nC charge at x = -4 m on the x axis,and a 70-nc charge at y = -6 m on the y axis.What is the electric potential (relative to a zero at infinity)at the point x = 8 m on the x axis?

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A series of 3 uncharged concentric spherical conducting shells surround a small central charge q.The potential at a point outside the third shell,at distance r from the center,and relative to V = 0 at $\infty$ ,is

To recharge a 12-V battery,a battery charger must move 3.6 * 10⁵ C of charge from the negative to the positive terminal.What amount of work is done by the battery charger? How many kilowatt hours is this?

A 0.16 pF parallel-plate capacitor is charged to 10 V.Then the battery is disconnected from the capacitor.When 1.00 *10⁷ electrons are now placed on the negative plate of the capacitor,the voltage between the plates changes by

Into the gap between the plates of a parallel plate capacitor of capacitance $C _ { 0 }$ a slab of metal is inserted halfway between the plates filling one fourth of the gap between the plates.What is the resulting new capacitance?

A particle (charge 7.5 $\mu$ C)is released from rest at a point on the x axis,x = 10 cm.It begins to move due to the presence of a 2.0- $\mu$ C charge which remains fixed at the origin.What is the kinetic energy of the particle at the instant it passes the point x = 1.0 m?

The electric field in a region of space is given by E_x = (3.0x)N/C,E_y = E_z = 0,where x is in m.Points A and B are on the x axis at x_A = 3.0 m and x_B = 5.0 m.Determine the potential difference V_B - V_A.

A 20- $\mu$ F capacitor charged to 2.0 kV and a 40- $\mu$ F capacitor charged to 3.0 kV are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final charge on the 20- $\mu$ F capacitor after the two are so connected?