Which equation correctly relates work, charge, and potential difference?

Which equation correctly relates work, charge, and potential difference?

• A. W = qV
• B. W = V/q
• C. W = q/E
• D. W = E/q

Answer: (A)

Work is the energy transferred when a charge moves through an electric potential difference. The potential difference V tells how much energy per unit charge is gained or lost in moving from one point to another. Therefore the total energy change for a charge q is the charge times that energy per charge, which gives W = qΔV. In introductory contexts, V is used to denote that potential difference, so W = qV is the correct relation. This has the right units: volts (Joules per coulomb) times coulombs gives joules. The other forms mix up the quantities or units. W = V/q would divide energy per charge by charge, not yielding energy. W = q/E or W = E/q introduce the electric field E (with units of V/m) in a way that doesn’t produce energy in joules.

Work is the energy transferred when a charge moves through an electric potential difference. The potential difference V tells how much energy per unit charge is gained or lost in moving from one point to another. Therefore the total energy change for a charge q is the charge times that energy per charge, which gives W = qΔV. In introductory contexts, V is used to denote that potential difference, so W = qV is the correct relation. This has the right units: volts (Joules per coulomb) times coulombs gives joules.

The other forms mix up the quantities or units. W = V/q would divide energy per charge by charge, not yielding energy. W = q/E or W = E/q introduce the electric field E (with units of V/m) in a way that doesn’t produce energy in joules.