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Worksheet: Electric Potential of a Charged Sphere

Q1:

A 0.500-cm-radius plastic sphere, used in a static electricity demonstration, has a uniformly distributed 40.0-pC charge on its surface. What is the electric potential just outside the sphere’s surface?

Q2:

A Van de Graaff generator has a 2.00-m-diameter metal sphere with 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?

The charge of an electron is C and the charge of a proton is C. An oxygen atom with eight protons and three missing electrons is released near the Van de Graaff generator. What is the electrical potential energy of 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 +3.0 µC is put on the surface of a hollow aluminum spherical ball which has a radius of 5.0 cm. The charge is in equilibrium at the outer surface of the ball.

Determine the magnitude of the electric field produced by this charge at a point 1.0 cm from the center of the aluminum ball.

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

Determine the magnitude of the electric field produced by this charge at a point 10 cm from the center of the aluminum ball.

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

Q4:

A charge of µC is distributed uniformly over the surface of a spherical volume of radius 10.0 cm.

Determine the electric field due to this charge at a distance of 2.0 cm from the center of the sphere.

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

Determine the electric field due to this charge at a distance of 5.0 cm from the center of the sphere.

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

Determine the electric field due to this charge at a distance of 20.0 cm from the center of the sphere.

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

Q5:

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

Q6:

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

Q7:

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?

Q8:

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.

  • A N/C
  • B N/C
  • C 0.0 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

Q9:

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 ?

Q10:

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

Q11:

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?