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


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) decreasing magnitude of the electric field.

F) C) and D)
G) A) and B)

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Identical 4.0-μC charges are placed on the y axis at y = ±4.0 m. Point A is on the x axis at x = +3.0 m. Determine the electric potential of point A (relative to zero at the origin) .


A) −4.5 kV
B) −2.7 kV
C) −1.8 kV
D) −3.6 kV
E) −14 kV

F) A) and B)
G) None of the above

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Two charges lie on the x axis, +2q at the origin, and −3q at x = 5.0 m. The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero) is


A) 1.0 m.
B) 2.0 m.
C) 2.5 m.
D) 3.0 m.
E) 4.0 m.

F) A) and B)
G) C) and D)

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A particle (mass = 6.7 × 10−27 kg, charge = 3.2 × 10−19 C) moves along the positive x axis with a speed of 4.8 × 105 m/s. It enters a region of uniform electric field parallel to its motion and comes to rest after moving 2.0 m into the field. What is the magnitude of the electric field?


A) 2.0 kN/C
B) 1.5 kN/C
C) 1.2 kN/C
D) 3.5 kN/C
E) 2.4 kN/C

F) A) and D)
G) A) and C)

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A point charge of 6.0 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm, outer radius = 2.0 cm) which has a net charge of −4.0 nC. Determine the resulting charge density on the inner surface of the conducting sphere.


A) +4.8 μC/m2
B) −4.8 μC/m2
C) −9.5 μC/m2
D) +9.5 μC/m2
E) −8.0 μC/m2

F) D) and E)
G) C) and D)

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The gap between electrodes in a spark plug is 0.06 cm. In order to produce an electric spark in a gasoline-air mixture, the electric field must reach a value of 3 × 106 V/m. What minimum voltage must be supplied by the ignition circuit when starting the car?

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A particle (charge 7.5 μC) 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-μC 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?


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

F) A) and B)
G) A) and C)

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When introduced into a region where an electric field is present, an electron with initial velocity When introduced into a region where an electric field is present, an electron with initial velocity   will eventually move A)  along an electric field line, in the positive direction of the line. B)  along an electric field line, in the negative direction of the line. C)  to a point of decreased potential. D)  to a point of increased potential. E)  as described in both (b)  and (d) . will eventually move


A) along an electric field line, in the positive direction of the line.
B) along an electric field line, in the negative direction of the line.
C) to a point of decreased potential.
D) to a point of increased potential.
E) as described in both (b) and (d) .

F) A) and B)
G) B) and D)

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


A) loses 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) loses 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.

F) None of the above
G) B) and C)

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Two charges lie on the x axis, +3q at the origin, and −2q at x = 5.0 m. The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero) is


A) 1.0 m.
B) 2.0 m.
C) 2.5 m.
D) 3.0 m.
E) 4.0 m.

F) D) and E)
G) C) and D)

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Identical point charges (+20 μC) are placed at the corners of an equilateral triangle with sides of 2.0-m length. How much external energy is required to bring a charge of 45 μC from infinity to the midpoint of one side of the triangle?


A) 26 J
B) 16 J
C) 23 J
D) 21 J
E) 12 J

F) C) and D)
G) A) and B)

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When a charged particle is moved along an electric field line,


A) the electric field does no work on the charge.
B) the electrical potential energy of the charge does not change.
C) the electrical potential energy of the charge undergoes the maximum change in magnitude.
D) the voltage changes, but there is no change in electrical potential energy.
E) the electrical potential energy undergoes the maximum change, but there is no change in voltage.

F) All of the above
G) B) and D)

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The electric potential inside a charged solid spherical conductor in equilibrium


A) is always zero.
B) is constant and equal to its value at the surface.
C) decreases from its value at the surface to a value of zero at the center.
D) increases from its value at the surface to a value at the center that is a multiple of the potential at the surface.
E) is equal to the charge passing through the surface per unit time divided by the resistance.

F) A) and C)
G) C) and D)

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A charge of 20 nC is distributed uniformly along the x axis from x = −2.0 m to x = +2.0 m. What is the electric potential (relative to zero at infinity) at the point x = 5.0 m on the x axis?


A) 57 V
B) 48 V
C) 38 V
D) 67 V
E) 100 V

F) A) and E)
G) A) and D)

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An uncharged metal sphere is placed on an insulating puck on a frictionless table. While being held parallel to the table, a rod with a charge q is brought close to the sphere, but does not touch it. As the rod is brought in, the sphere


A) remains at rest.
B) moves toward the rod.
C) moves away from the rod.
D) moves perpendicular to the velocity vector of the rod.
E) moves upward off the puck.

F) A) and B)
G) None of the above

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Four electrons move from point A to point B in a uniform electric field as shown below. Rank the electrons in diagrams I through IV by the changes in potential energy from most positive to most negative when traveling from A to B. Four electrons move from point A to point B in a uniform electric field as shown below. Rank the electrons in diagrams I through IV by the changes in potential energy from most positive to most negative when traveling from A to B.   A)  I = II = III = IV. B)  II = III > I > IV. C)  III > I = IV > II. D)  II > I = IV > III. E)  I > II = III > IV.


A) I = II = III = IV.
B) II = III > I > IV.
C) III > I = IV > II.
D) II > I = IV > III.
E) I > II = III > IV.

F) A) and C)
G) All of the above

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The Bohr model pictures a hydrogen atom in its ground state as a proton and an electron separated by the distance a0 = 0.529 × 10−10 m. The electric potential created by the electron at the position of the proton is


A) −13.6 V.
B) +13.6 V.
C) −27.2 V.
D) +27.2 V.
E) +5.12 × 109 V.

F) C) and E)
G) C) and D)

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A proton (mass = 1.67 × 10−27 kg, charge = 1.60 × 10−19 C) moves from point A to point B under the influence of an electrostatic force only. At point A the proton moves with a speed of 60 km/s. At point B the speed of the proton is 80 km/s. Determine the potential difference VB − VA.


A) +15 V
B) −15 V
C) −33 V
D) +33 V
E) −20 V

F) C) and D)
G) B) and E)

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A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m3. What is the magnitude of the potential difference between the center and a point 4.0 cm away?


A) 12 V
B) 6.8 V
C) 3.0 V
D) 4.7 V
E) 2.2 V

F) A) and B)
G) A) and E)

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When introduced into a region where an electric field is present, a proton with initial velocity When introduced into a region where an electric field is present, a proton with initial velocity   will eventually move A)  along an electric field line, in the positive direction of the line. B)  along an electric field line, in the negative direction of the line. C)  to a point of decreased potential. D)  as described in both (a)  and (c) . will eventually move


A) along an electric field line, in the positive direction of the line.
B) along an electric field line, in the negative direction of the line.
C) to a point of decreased potential.
D) as described in both (a) and (c) .

E) B) and C)
F) All of the above

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