Exam 25: Electric Potential

A particle (charge = +2.0 mC) moving in a region where only electric forces act on it has a kinetic energy of 5.0 J at point A. The particle subsequently passes through point B which has an electric potential of +1.5 kV relative to point A. Determine the kinetic energy of the particle as it moves through point B.

Point charges of equal magnitudes (25 nC) and opposite signs are placed on (diagonally) opposite corners of a 60-cm × 80-cm rectangle. If point A is the corner of this rectangle nearest the positive charge and point B is located at the intersection of the diagonals of the rectangle, determine the potential difference, V_B − V_A.

Several charges in the neighborhood of point P produce an electric potential of 6.0 kV (relative to zero at infinity) and an electric field of N/C at point P. Determine the work required of an external agent to move a 3.0-μC charge along the x axis from infinity to point P without any net change in the kinetic energy of the particle.

The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C. What is the charge density on the surface of the cylinder?

A series of 3 uncharged concentric shells surround a small central charge q. The charge distributed on the outside of the third shell is

In the Bohr model of the hydrogen atom, the electron circles the proton at a distance of 0.529 × 10−¹⁰ m. Find the potential at the position of the electron.

A charge of 18 nC is uniformly distributed along the y axis from y = 3 m to y = 5 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +2 m on the x axis?

A charge is placed on a spherical conductor of radius r₁. This sphere is then connected to a distant sphere of radius r₂ (not equal to r₁) by a conducting wire. After the charges on the spheres are in equilibrium,

Charge of uniform density 90 nC/m³ is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 2.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis).

Three identical point charges (+2.0 nC) are placed at the corners of an equilateral triangle with sides of 2.0-m length. If the electric potential is taken to be zero at infinity, what is the potential at the midpoint of any one of the sides of the triangle?

A particle (charge = 50 μC) moves in a region where the only force on it is an electric force. As the particle moves 25 cm from point A to point B, its kinetic energy increases by 1.5 mJ. Determine the electric potential difference, V_B − V_A.

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 50 km/s. At point B the speed of the proton is 80 km/s. Determine the potential difference V_B − V_A.

The axis of a long hollow metallic cylinder (inner radius = 1.0 cm, outer radius = 2.0 cm) coincides with a long wire. The wire has a linear charge density of −8.0 pC/m, and the cylinder has a net charge per unit length of −4.0 pC/m. Determine the magnitude of the electric field 3.0 cm from the axis.

If the electric field just outside a thin conducting sheet is equal to 1.5 N/C, determine the surface charge density on the conductor.

Two particles, each having a mass of 3.0 μg and having equal but opposite charges of magnitude of 6.0 nC, are released simultaneously from rest when they are a very large distance apart. What distance separates the two at the instant when each has a speed of 5.0 m/s?

Which of the following represents the equipotential lines of a dipole?

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

Charge of uniform linear density 3.0 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 x = +4 m on the x axis?

For the potential , what is the corresponding electric field at the point (2,2,2)?

A particle (charge = 5.0 μC) is released from rest at a point x = 10 cm. If a 5.0-μC charge is held fixed at the origin, what is the kinetic energy of the particle after it has moved 90 cm?