# Worksheet: Electric Potential of a Charged Sphere

In this worksheet, we will practice determining the electric potential around an electrically charged sphere, using symmetries to simplify calculations.

Q1:

A plastic sphere of radius 0.250 cm, used in a static electricity demonstration, has a uniformly distributed charge of 40.0 pC on its surface. What is the electric potential just outside the sphere’s surface?

Q2:

A Van de Graaff generator has a metal sphere with a diameter of 2.00 m and a charge of 5.00 mC on it.

What is the potential near its surface?

At what distance from its center is the potential 1.00 MV?

An oxygen atom with eight protons and three missing electrons is released near the Van de Graaff generator. What is the kinetic energy this atom when it is at a distance from the generator for which the potential of the electric field around the generator is 1.00 MV?

Q3:

A charge of µC is distributed uniformly throughout a spherical volume of radius 18.0 cm. The electric field due to this charge varies with distance from the center of the sphere.

Find the magnitude of the electric field 3.5 cm from the center of the sphere.

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

Find the magnitude of the electric field 9.0 cm from the center of the sphere.

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

Find the magnitude of the electric field 21 cm from the center of the sphere.

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

Q4:

A point charge is placed at the center of a spherical conducting shell of inner radius 2.5 cm and of outer radius 5.3 cm. The electric field just above the surface of the conductor is directed radially outward and has a magnitude of 9.7 N/C .

What is the charge on the inner surface of the shell?

• A C
• B C
• C C
• D C
• E C

What is the charge on the outer surface of the shell?

• A C
• B C
• C C
• D C
• E C

What is the net charge on the conductor?

• A C
• B C
• C C
• D C
• E C

Q5:

A metallic sphere of radius 1.3 cm is charged with a µC charge, which spreads on the surface of the sphere uniformly. The metallic sphere stands on an insulated stand and is surrounded by a larger metallic spherical shell of inner radius 7.0 cm and outer radius 8.0 cm. Now, a charge of µC is placed on the inside of the spherical shell, which spreads out uniformly on the inside surface of the shell. Assume the potential is zero at infinity.

What is the potential of the spherical shell?

What is the potential at the surface of the sphere?

What is the potential at cm?

Q6:

A point charge is placed at the center of an uncharged spherical conducting shell of inner radius 4.6 cm and of outer radius 8.8 cm.

Find the magnitude of the electric field 4.9 cm from the point charge.

• A0.0 N/C
• B N/C
• C N/C
• D N/C
• E N/C

Find the magnitude of the electric field 7.3 cm from the point charge.

Find the magnitude of the electric field 9.3 cm from the point charge.

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

What charge is induced on the inner surface of the shell?

• A C
• B C
• C C
• D C
• E C

What charge is induced on the outer surface of the shell?

• A C
• B C
• C C
• D C
• E C

Q7:

A Van de Graaff generator holds a charge of 5.20 mC. A point is located at a distance of 7.12 m from the center of the generator’s top terminal.

What is the magnitude of the electric field at the point ?

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

What is the magnitude of the force exerted by the generator’s top terminal on a 4.51 µC charge located at the point ?

Q8:

Find the electric potential negligibly far outside a 23.0 cm diameter metal sphere that has a net positive charge of 3.4 µC.

Q9:

How much energy is stored in the electric field of a metal sphere of radius 1.0 m that is kept at a 42 V potential?

Q10:

An aluminum spherical ball of radius 4.3 cm is charged by 8.4 µC. A copper spherical shell of inner radius 6.3 cm and outer radius 9.0 cm surrounds the ball. A total charge of µC is put on the copper shell.

Find the magnitude of the electric field 5.0 cm from the ball’s center.

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

Find the magnitude of the electric field 12 cm from the ball’s center.

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

Q11:

Two concentric spherical shells of negligible thicknesses have radii and . The inner and outer shells carry net charges of 3.3 mC and 4.5 mC respectively. What is the electric potential at ?

What is the electric potential at ?

What is the electric potential at ?

Q12:

Concentric conducting spherical shells carry charges and of 12 µC, respectively, as shown in the diagram. The inner shell has a negligible thickness and a radius of . The inner surface of the outer shell is from the center of the inner shell and the outer surface at from the inner shell’s center. Determine the magnitude of the electric field at a distance of 2.0 cm from the center of the sphere.

Determine the magnitude of the electric field at a distance of 5.0 cm from the center of the sphere.

• A N/C
• B N/C
• C0.0 N/C
• D N/C
• E N/C

Determine the magnitude of the electric field at a distance of 7.0 cm from the center of the sphere.

Determine the magnitude of the electric field at a distance 9.0 cm from the center of the sphere.

Q13:

Two nonconducting spheres of radii and are uniformly charged with charge densities and respectively. They are separated at a center-to-center distance , as shown in the diagram. Find the magnitude of the electric field at point located at a distance from the centers of both spheres, where point is directed at from the line joining the two spheres. Assume that the charge densities of the spheres are not affected by the presence of each other. • A N/C
• B N/C
• C N/C
• D N/C
• E N/C

Q14:

Suppose that the charge density of the spherical charge distribution shown in the diagram is for , where and .

Find the electric field magnitude where cm.

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

Find the electric field magnitude where cm.

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C