Exam 19: Electric Potential Energy and the Electric Potential

The plates of a parallel plate capacitor each have an area of 0.40 m² and are separated by a distance of 0.02 m. They are charged until the potential difference between the plates is 3000 V. The charged capacitor is then isolated. -Suppose that a dielectric sheet is inserted to completely fill the space between the plates and the potential difference between the plates drops to 1000 V. What is the capacitance of the system after the dielectric is inserted?

A charge q = -6.0 µC is moved 0.25 m horizontally to point P in a region where an electric field is 250 V/m directed vertically, as shown. What is the change in the electric potential energy of the charge?

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I. -A positive point charge is placed at F. Complete the following statement: When it is released,

A proton moves in a constant electric field from point A to point B. The magnitude of the electric field is 6.4 × 10⁴ N/C; and it is directed as shown in the drawing, the direction opposite to the motion of the proton. If the distance from point A to point B is 0.50 m, what is the change in the proton's electric potential energy, EPE_A - EPE_B?

A parallel plate capacitor with plates of area A and plate separation d is charged so that the potential difference between its plates is V. If the capacitor is then isolated and its plate separation is decreased to d/2, what happens to its capacitance?

A parallel plate capacitor has plates of area 2.0 × 10^-3 m² and plate separation 1.0 × 10^-4 m. Determine the capacitance of this system if air fills the volume between the plates.

The figure below shows four parallel plate capacitors: A, B, C, and D. Each capacitor carries the same charge q and has the same plate area A. As suggested by the figure, the plates of capacitors A and C are separated by a distance d while those of B and D are separated by a distance 2d. Capacitors A and B are maintained in vacuum while capacitors C and D contain dielectrics with constant  = 5. -Which capacitor is storing the greatest amount of electric potential energy?

Two positive charges are located at points A and B as shown in the figure. The distance from each charge to the point P is a = 2.0 m. -Suppose that the charges are rearranged as shown in this figure. Which one of the following statements is true for this new arrangement?

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I. -What is the potential difference between points B and E?

A parallel plate capacitor with plates of area A and plate separation d is charged so that the potential difference between its plates is V. If the capacitor is then isolated and its plate separation is decreased to d/2, what happens to the potential difference between the plates?

Which one of the following changes will necessarily increase the capacitance of a capacitor?

Two point charges are held at the corners of a rectangle as shown in the figure. The lengths of sides of the rectangle are 0.050 m and 0.150 m. Assume that the electric potential is defined to be zero at infinity. -What is the potential difference, V_B - V_A, between corners A and B?

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I. -What is the magnitude of the electric field at point A?

Two positive point charges are separated by a distance R. If the distance between the charges is reduced to R/2, what happens to the total electric potential energy of the system?

A charge is located at the center of sphere A (radius R_A = 0.0010 m), which is in the center of sphere B (radius R_B = 0.0012 m). Spheres A and B are both equipotential surfaces. What is the ratio V_A/V_B of the potentials of these surfaces?

Two point charges are held at the corners of a rectangle as shown in the figure. The lengths of sides of the rectangle are 0.050 m and 0.150 m. Assume that the electric potential is defined to be zero at infinity. -Determine the electric potential at corner A.

A uniform electric field of 8 V/m exists between the plates of a parallel plate capacitor. How much work is required to move a +20 $\mu$ C point charge from the negative plate to the positive plate if the plate separation is 0.050 m?

The plates of a parallel plate capacitor each have an area of 0.40 m² and are separated by a distance of 0.02 m. They are charged until the potential difference between the plates is 3000 V. The charged capacitor is then isolated. -Determine the magnitude of the charge on either capacitor plate.

The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I. -What is the direction of the electric field at B?

Two charges of opposite sign and equal magnitude Q = 0.82 C are held 2.0 m apart as shown in the figure. -Determine the magnitude of the electric field at the point P.