A test charge q is moved through a potential difference ΔV by an external agent. What is the work done by the external agent?

A test charge q is moved through a potential difference ΔV by an external agent. What is the work done by the external agent?

• A. W_ext = q ΔV
• B. W_ext = ΔV / q
• C. W_ext = q^2 ΔV
• D. W_ext = ΔV

Answer: (A)

Moving a charge through a potential difference changes its electric potential energy by ΔU = q ΔV. If you move the charge slowly so its kinetic energy stays the same, the work you do is exactly this change in potential energy, so W_ext = ΔU = q ΔV. The units also line up: volts times coulombs give joules, which are units of energy. The other expressions don’t have the right units or physical meaning for work in this context.

Moving a charge through a potential difference changes its electric potential energy by ΔU = q ΔV. If you move the charge slowly so its kinetic energy stays the same, the work you do is exactly this change in potential energy, so W_ext = ΔU = q ΔV. The units also line up: volts times coulombs give joules, which are units of energy. The other expressions don’t have the right units or physical meaning for work in this context.