Which statement best describes the relationship between electric potential energy and electric potential?

Which statement best describes the relationship between electric potential energy and electric potential?

• A. Electric potential energy is the energy per unit charge; electric potential is the total energy.
• B. Electric potential energy is the energy due to position in an electric field; electric potential is energy per unit charge at that position.
• C. Electric potential energy and electric potential are identical.
• D. Electric potential energy is the derivative of electric potential.

Answer: (B)

Electric potential energy and electric potential are related through the amount of charge involved. Electric potential energy is the energy a charge has because of its position in an electric field; it depends on both the field location and how much charge you have. Electric potential, or voltage, is the energy per unit charge at that location. Mathematically, U = qV, so the potential energy scales with the charge, while the potential itself is a property of the location in the field and does not depend on how much charge you place there. For example, if a location in the field has a potential of 5 volts, a 2-coulomb charge there has potential energy U = qV = 2 × 5 = 10 joules, while a 1-coulomb charge would have U = 1 × 5 = 5 joules. The potential at that point remains 5 volts regardless of the test charge, illustrating the distinction between energy per unit charge and total energy.

Electric potential energy and electric potential are related through the amount of charge involved. Electric potential energy is the energy a charge has because of its position in an electric field; it depends on both the field location and how much charge you have. Electric potential, or voltage, is the energy per unit charge at that location. Mathematically, U = qV, so the potential energy scales with the charge, while the potential itself is a property of the location in the field and does not depend on how much charge you place there.

For example, if a location in the field has a potential of 5 volts, a 2-coulomb charge there has potential energy U = qV = 2 × 5 = 10 joules, while a 1-coulomb charge would have U = 1 × 5 = 5 joules. The potential at that point remains 5 volts regardless of the test charge, illustrating the distinction between energy per unit charge and total energy.