Physics

Physics

Problem

Which equation correctly relates the change in electric potential energy ΔU\Delta U of a test charge qq to the corresponding electric potential difference ΔV\Delta V between two points? a) ΔV=−ΔUq\displaystyle \Delta V = -\dfrac{\Delta U}{q} b) ΔV=ΔU∣q∣\displaystyle \Delta V = \dfrac{\Delta U}{|q|} c) ΔV=ΔUq\displaystyle \Delta V = \dfrac{\Delta U}{q} d) ΔV=12 ΔUq\displaystyle \Delta V = \dfrac{1}{2}\,\dfrac{\Delta U}{q}
Intuitive explanation

The key insight is that electric potential is simply potential energy per unit charge—it's the "work per coulomb" that the field does. So if you know the potential difference between two points, multiplying by the charge tells you how much energy that charge gains or loses moving between them. The relationship is linear and direct: potential difference scales the energy change.

Intuitive explanation

The key insight is that electric potential is simply potential energy per unit charge—it's the "work per coulomb" that the field does. So if you know the potential difference between two points, multiplying by the charge tells you how much energy that charge gains or loses moving between them. The relationship is linear and direct: potential difference scales the energy change.

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