Worksheet: Electric Potential Difference

In this worksheet, we will practice calculating the change in the electric potential energy per unit charge given a change in position in an electric field.


Two parallel plates, each with sides of length 10 cm are given equal and opposite charges of magnitude 5.0×10 C. The plates are 1.5 mm apart. What is the potential difference between the plates?


The electric field strength between two parallel conducting plates separated by 4.00 cm is 7.50×10/Vm.

What is the potential difference between the plates?

The plate with the lowest potential is taken as zero potential. What is the electrical potential 1.00 cm from the zero potential plate and 3.00 cm from the other plate?


Two parallel conducting plates are separated by 10.0 cm, and one of them is taken to be at 0 volt.

What is the electric field strength between them, if the potential 8.00 cm from the 0 volt plate (and 2.00 cm from the other) is 450 V?

  • A5.62×10 kV/m
  • B9.75 kV/m
  • C1.80 kV/m
  • D3.66 kV/m
  • E8.00 kV/m

What is the voltage between the plates?


Two parallel conducting pates, each of cross-sectional area 400 cm2, are 2.0 cm apart and uncharged. 1.0×10 electrons are transferred from one of the plates to the other plate.

What is the potential difference between the plates?

  • A4.3×10 V
  • B5.7×10 V
  • C3.0×10 V
  • D7.3×10 V
  • E9.0×10 V

What is the potential difference between the positively charged plate and a point between the plates that is 1.25 cm away from the positively charged plate and 0.75 cm away from the negatively charged plate?

  • A6.7×10 V
  • B4.1×10 V
  • C5.0×10 V
  • D5.7×10 V
  • E7.6×10 V


A lightning bolt strikes a tree, moving 20.0 C of charge through a potential difference of 1.00×10 MV.

How much energy was dissipated by the lightning strike?

  • A2.00×10 J
  • B1.78×10 J
  • C2.22×10 J
  • D5.00×10 J
  • E9.00×10 J

Assume that all of the energy supplied to the charge in the lightning strike is converted to heat. The specific heat capacity of water is 4,186 J/kg⋅C and the specific latent heat of vaporization of water is 2,258 kJ/kg. What mass of water could be raised from 15.0 to its boiling point and then boiled by this energy?


What is the potential between two points situated 10 cm and 20 cm from a 3.0-µC point charge?


Two parallel conducting plates are separated by a distance of 2.0 mm, and a potential difference of 5.0×10 V is applied.

What is the electric field strength between the plates?

  • A2.5×10 V/m
  • B2.2×10 V/m
  • C3.0×10 V/m
  • D2.0×10 V/m
  • E1.0×10 V/m

What is the minimum separation of the plates that produces an electric field strength that does not exceed 3.0×10 V/m?


Two parallel conducting plates are separated by 1.00 cm and have a potential difference between them of 2.36×10 V. What is the magnitude of the electric field between the plates?

  • A2.36×10 V/m
  • B3.33×10 V/m
  • C1.44×10 V/m
  • D1.86×10 V/m
  • E2.25×10 V/m


The wall of a cell is 8.81 nm thick and the potential difference across it is 74.0 mV. Modeling the cell wall as a pair of parallel plates, what is the magnitude of the electric field within the wall?

  • A8.40×10 V/m
  • B2.66×10 V/m
  • C2.53×10 V/m
  • D8.24×10 V/m
  • E5.53×10 V/m


Two parallel conducting plates are separated by a 0.384 cm thick gap of air. If the greatest electric field magnitude in which the air can act as an insulator is 3.00×10 V/m, what is the maximum potential difference that can be applied across the plates that allows them to function as a capacitor?


Singly charged gas ions are accelerated from rest through a voltage of 12.5 V. At what temperature will the average kinetic energy of gas molecules be the same as that of these ions?


A simple and common technique for accelerating electrons is shown in the figure, where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving. What is the acceleration of the electron if the field strength is 4.6×10 N/C?

  • A7.6×10 m/s2
  • B6.5×10 m/s2
  • C4.7×10 m/s2
  • D8.1×10 m/s2
  • E5.2×10 m/s2


At electric field magnitudes greater than 4.25×10 N/C, atoms in a certain gas will ionize and produce discharge arcs. In an electric field of this magnitude, through what distance would an initially at-rest proton need to move in order to accelerate to the speed of light, neglecting relativistic effects?


A certain fully ionized helium nucleus has a positive charge of 2𝑒 and a mass of 6.64×10 kg and is moving at a speed negligibly less than the speed of light. Neglect relativistic effects when modeling the energy of the nucleus.

What is the kinetic energy of the nucleus in joules?

  • A4.74×10 J
  • B6.04×10 J
  • C3.89×10 J
  • D3.33×10 J
  • E2.33×10 J

What is the kinetic energy of the nucleus in electronvolts?

Starting from rest, through what potential difference would the nucleus need to be accelerated to reach this speed?


How far apart are two conducting plates that have an electric field strength of 7.25×10 V/m between them if the potential difference across them is 15.0 kV?


Membrane walls of living cells have electric fields across them due to separation of ions across the membranes. Calculate the potential difference across a 7.85 nm thick membrane if the electric field strength within the membrane is a uniform 6.11 MV/m.


The temperature in the core region of a star is modeled as being 3.5×10C. A singly charged ion at rest could be accelerated by a potential difference that would give the ion kinetic energy equal to the average kinetic energy of ions found in the star’s core region. What potential difference is required to produce that energy?

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