What is the difference between electric potential energy and electric potential?

What is the difference between electric potential energy and electric potential?

• A. Electric potential energy is independent of charge, while electric potential is energy per unit charge.
• B. Electric potential energy equals electric potential times charge.
• C. Electric potential energy is the same as electric potential.
• D. Electric potential energy depends on charge; electric potential is energy per unit charge.

Answer: (D)

The key idea here is the difference between a field quantity and the energy of a specific charge in that field. Electric potential is the field’s work per unit charge at a point—how much energy per coulomb would be needed to bring a test charge to that point. It doesn’t depend on how large the test charge is. Electric potential energy, on the other hand, is the actual energy a particular charge q has because of its position in the field; it scales with how much charge you have. So, the potential is energy per unit charge, while the potential energy is the energy of the charge itself and hence depends on the amount of charge. For example, if the potential at a point is V, a charge q has potential energy U = qV; doubling q doubles the energy, but the potential V stays the same. That’s why the statement emphasizing that electric potential energy depends on charge and electric potential is energy per unit charge best captures the difference. While U = qV describes their relationship, the distinction is most clearly about what each quantity represents: energy that changes with the amount of charge vs a property of the field per unit charge.

The key idea here is the difference between a field quantity and the energy of a specific charge in that field. Electric potential is the field’s work per unit charge at a point—how much energy per coulomb would be needed to bring a test charge to that point. It doesn’t depend on how large the test charge is. Electric potential energy, on the other hand, is the actual energy a particular charge q has because of its position in the field; it scales with how much charge you have.

So, the potential is energy per unit charge, while the potential energy is the energy of the charge itself and hence depends on the amount of charge. For example, if the potential at a point is V, a charge q has potential energy U = qV; doubling q doubles the energy, but the potential V stays the same.

That’s why the statement emphasizing that electric potential energy depends on charge and electric potential is energy per unit charge best captures the difference. While U = qV describes their relationship, the distinction is most clearly about what each quantity represents: energy that changes with the amount of charge vs a property of the field per unit charge.