Worksheet: Absolute Electric Potential

In this worksheet, we will practice defining the absolute electric potential of a point charge in terms of the change in potential difference around the charge.

Q1:

A sphere has a surface uniformly charged with 1.00 C. At what distance from its centre is the potential 5.00 MV?

  • A 0.81 km
  • B 0.11 km
  • C 1.08 km
  • D 1.80 km
  • E 1.18 km

Q2:

If the absolute electric potential due to a point charge is 5 . 0 0 × 1 0 2 V at a distance of 15.0 m, what are the sign and magnitude of the charge?

  • A + 1 . 0 2 × 1 0 7 C
  • B + 3 . 7 1 × 1 0 7 C
  • C 2 . 5 7 × 1 0 7 C
  • D + 8 . 3 3 × 1 0 7 C
  • E 6 . 3 8 × 1 0 7 C

Q3:

Two charges of 2 . 0 µC and + 2 . 0 µC are separated by 4.0 cm on the 𝑧 -axis symmetrically about the origin, with the positive charge uppermost. Two points of interest 𝑃 1 and 𝑃 2 are located 3.0 cm and 30 cm from origin at an angle of 3 0 with respect to the 𝑧 -axis.

Evaluate the electric potential at 𝑃 1 .

  • A 9 . 0 × 1 0 5 V
  • B 8 . 3 × 1 0 5 V
  • C 1 . 1 × 1 0 6 V
  • D 7 . 4 × 1 0 5 V
  • E 1 . 3 × 1 0 6 V

Evaluate the electric potential at 𝑃 2 .

  • A 6 . 9 × 1 0 5 V
  • B 8 . 8 × 1 0 5 V
  • C 4 . 7 × 1 0 5 V
  • D 3 . 0 × 1 0 5 V
  • E 1 . 0 × 1 0 6 V

Q4:

In a particular region, the electric potential is given by , where , , and correspond to distances in meters. Find the electric field in V/m at a point in this region that has the coordinates .

  • A V/m
  • B V/m
  • C V/m
  • D V/m
  • E V/m

Q5:

A glass ring of radius 7.5 cm is painted with a charged paint such that the charge density around the ring varies continuously as a function of the polar angle 𝜃 , 𝜆 = 4 . 5 × 1 0 2 𝜃 / 6 c o s C m . Find the potential at a point 25 cm above the center.

Q6:

A small spherical pith ball of radius 0.36 cm is painted with a silver paint and then 8 . 0 µC of charge is applied to it. The charged pith ball is put at the center of a gold spherical shell of inner radius 3.0 cm and outer radius 3.3 cm. Find the electric potential at the surface of the gold shell with respect to zero potential at infinity.

  • A 4 . 1 MV
  • B 3 . 5 MV
  • C 3 . 1 MV
  • D 2 . 2 MV
  • E 1 . 2 MV

Q7:

A point charge 𝑞 = 9 . 2 × 1 0 8 C is placed at the center of an uncharged spherical conducting shell of inner radius 7.0 cm and outer radius 8.5 cm. The points 𝑃 1 , 𝑃 2 , and 𝑃 3 are at distances of 5.0 cm, 7.5 cm, and 13.5 cm, respectively, from the point charge.

What is the electric potential at 𝑃 1 ?

What is the electric potential at 𝑃 2 ?

What is the electric potential at 𝑃 3 ?

Q8:

An electron and a proton, each starting from rest, are accelerated by the same uniform electric field of 400.0 N/C.

Determine the distance traveled through the electric field by the electron when its kinetic energy is 6 . 9 0 × 1 0 1 6 J.

For how long has the electron been accelerated by the electric field when its kinetic energy is 6 . 9 0 × 1 0 1 6 J?

  • A 5 . 5 0 × 1 0 7 s
  • B 6 3 . 0 × 1 0 6 s
  • C 1 2 . 0 × 1 0 7 s
  • D 9 . 4 2 × 1 0 7 s
  • E 6 3 . 0 × 1 0 7 s

Determine the distance traveled through the electric field by the proton when its kinetic energy is 6 . 9 0 × 1 0 1 6 J.

For how long has the proton been accelerated by the electric field when its kinetic energy is 6 . 9 0 × 1 0 1 6 J?

  • A 2 . 3 7 × 1 0 5 s
  • B 9 8 . 1 × 1 0 5 s
  • C 9 8 . 2 × 1 0 5 s
  • D 6 3 . 2 × 1 0 5 s
  • E 4 5 . 2 × 1 0 5 s

Q9:

Three 5.0 µC charges are fixed at the vertices of a triangle that has 3.0 cm long sides. Find the total electric potential energy of the system.

Q10:

What is the magnitude of a point charge that produces a potential of 7.47 V at a distance of 2.63 mm?

  • A 3 . 1 2 × 1 0 1 2 C
  • B 1 . 9 4 × 1 0 1 2 C
  • C 5 . 7 4 × 1 0 1 2 C
  • D 2 . 1 9 × 1 0 1 2 C
  • E 4 . 3 0 × 1 0 1 2 C

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