Exam 25: Electric Potential

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 charge of 40 pC is distributed on an isolated spherical conductor that has a 4.0-cm radius. Point A is 1.0 cm from the center of the conductor and point B is 5.0 cm from the center of the conductor. Determine the electric potential difference V_A − V_B.

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 long cylindrical conductor (radius = 1.0 mm) carries a charge density of 4.0 pC/m and is inside a coaxial, hollow, cylindrical conductor (inner radius = 3.0 mm, outer radius = 4.0 mm) that has a total charge of −8.0 pC/m. What is the magnitude of the electric field 2.0 mm from the axis of these conductors?

Particle A (mass = m, charge = Q) and B (mass = m, charge = 5 Q) are released from rest with the distance between them equal to 1.0 m. If Q = 12 μC, what is the kinetic energy of particle B at the instant when the particles are 3.0 m apart?

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

A charged particle (q = −8.0 mC), which moves in a region where the only force acting on the particle is an electric force, is released from rest at point A. At point B the kinetic energy of the particle is equal to 4.8 J. What is the electric potential difference V_B − V_A?

A 4.0-pC point charge is placed at the center of a hollow (inner radius = 2.0 cm, outer radius = 4.0 cm) conducting sphere which has a net charge of 4.0 pC. Determine the magnitude of the electric field at a point which is 6.0 cm from the point charge.

A proton (m = 1.7 × 10−²⁷ kg, q = +1.6 × 10−¹⁹ C) starts from rest at point A and has a speed of 40 km/s at point B. Only electric forces act on it during this motion. Determine the electric potential difference V_B − V_A.

How much electrical charge is needed to raise an isolated metal sphere of radius 1.0 m to a potential of 1.0 × 10⁶ V?

A series of n uncharged concentric shells surround a small central charge q. The charge distributed on the outside of the nth shell is

A spherical conductor (radius = 1.0 cm) with a charge of 2.0 pC is within a concentric hollow spherical conductor (inner radius = 3.0 cm, outer radius = 4.0 cm) which has a total charge of −3.0 pC. What is the magnitude of the electric field 2.0 cm from the center of these conductors?

If a = 30 cm, b = 20 cm, q = +2.0 nC, and Q = −3.0 nC in the figure, what is the potential difference V_A − V_B?

A nonuniform linear charge distribution given by λ(x) = bx, where b is a constant, is distributed along the x axis from x = 0 to x = +L. If b = 40 nC/m² and L = 0.20 m, what is the electric potential (relative to a potential of zero at infinity) at the point y = 2L on the y axis?

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

Points A [at (3, 6) m] and B [at (8, −3) m] are in a region where the electric field is uniform and given by N/C. What is the electric potential difference V_A − V_B?

Identical 2.0-μC charges are located on the vertices of a square with sides that are 2.0 m in length. Determine the electric potential (relative to zero at infinity) at the center of the square.

A small metal sphere is suspended from the conducting cover of a conducting metal ice bucket by a non-conducting thread. The sphere is given a negative charge before the cover is placed on the bucket. The bucket is tilted by means of a non-conducting material so that the charged sphere touches the inside of the bucket. Which statement is correct?

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?

Charge of uniform density (3.5 nC/m) is distributed along the circular arc shown. Determine the electric potential (relative to zero at infinity) at point P.