Exam 19: Electric Potential Energy and the Electric Potential

An isolated system consists of two conducting spheres A and B. Sphere A has five times the radius of sphere B. Initially, the spheres are given equal amounts of positive charge and are isolated from each other. The two spheres are then connected by a conducting wire. Note: The potential of a sphere of radius R that carries a charge Q is V = kQ/R, if the potential at infinity is zero. -Which one of the following statements is true after the spheres are connected by the wire?

An isolated system consists of two conducting spheres A and B. Sphere A has five times the radius of sphere B. Initially, the spheres are given equal amounts of positive charge and are isolated from each other. The two spheres are then connected by a conducting wire. Note: The potential of a sphere of radius R that carries a charge Q is V = kQ/R, if the potential at infinity is zero. -Determine the ratio of the charge on sphere A to that on sphere B, q_A/q_B, after the spheres are connected by the wire.

A potential difference of 120 V is established between two parallel metal plates. The magnitude of the charge on each plate is 0.020 C. What is the capacitance of this capacitor?

P and Q are points within a uniform electric field that are separated by a distance of 0.2 m as shown. The potential difference between P and Q is 75 V. -How much work is required to move a +150 $\mu$ C point charge from P to Q?

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. -How much work is required to move a -1.0 $\mu$ C charge from A to E?

Two point charges are separated by 1.00 × 10-2 m. One charge is -2.8 × 10-8 C; and the other is +2.8 × 10-8 C. The points A and B are located 2.5 × 10-3 m from the lower and upper point charges as shown. -If a proton, which has a charge of +1.60 × 10^-19 C, is moved from rest at A to rest at B, what is change in electrical potential energy of the proton?

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 has the largest potential difference between its plates?

If the work required to move a +0.25 C charge from point A to point B is +175 J, what is the potential difference between the two points?

A completely ionized beryllium atom (net charge = +4e) is accelerated through a potential difference of 6.0 V. What is the increase in kinetic energy of the atom?

A capacitor has a very large capacitance of 10 F. The capacitor is charged by placing a potential difference of 2 V between its plates. How much energy is stored in the capacitor?

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. -At which of the labeled points will the electric field have the greatest magnitude?

A parallel plate capacitor is fully charged at a potential V. A dielectric with constant $\kappa$ = 4 is inserted between the plates of the capacitor while the potential difference between the plates remains constant. Which one of the following statements is false concerning this situation?

Two point charges are separated by 1.00 × 10-2 m. One charge is -2.8 × 10-8 C; and the other is +2.8 × 10-8 C. The points A and B are located 2.5 × 10-3 m from the lower and upper point charges as shown. -If an electron, which has a charge of 1.60 × 10^-19 C, is moved from rest at A to rest at B, what is the change in electric potential energy of the electron?

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 list below places the capacitors in order of increasing capacitance?

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. -Determine the electric potential at the point P.

A capacitor is initially charged to 3 V. It is then connected to a 6 V battery. What is the ratio of the final to the initial energy stored in the 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 electric potential energy of a +3.0 $\mu$ C charge placed at corner A?

Two point charges are located at two of the vertices of a right triangle, as shown in the figure. If a third charge -q is brought from infinity and placed at the third vertex, what will its electric potential energy be? Use the following values: a = 0.35 m; b = 0.65 m, and q = 3.0 × 10^-6 C.

The electric potential at a certain point is space is 12 V. What is the electric potential energy of a -3.0 $\mu$ C charge placed at that point?

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. -How much work is required to move a -1.0 $\mu$ C charge from B to D to C?