Physics

Physics

Problem

Two particles, one with charge +2.0 μC+2.0\,\mu\text{C} and the other with charge −3.0 μC-3.0\,\mu\text{C}, are each moved from point X to point Y, where the electric potential at Y is 150 V150\,\text{V} higher than at X. What is the ratio ΔU+ΔU−\displaystyle \frac{\Delta U_{+}}{\Delta U_{-}} of their changes in electric potential energy? a) +0.67+0.67 b) −1.5-1.5 c) −0.67-0.67 d) +0.44+0.44
Intuitive explanation

The key insight is that electric potential energy change depends on both the charge and the potential difference—but the potential difference is the same for both particles since they travel between the same two points. So the ratio of their energy changes is simply the ratio of their charges. Notice that charge is signed: the positive charge gains energy moving to higher potential, while the negative charge loses it, giving opposite signs to their changes.

Intuitive explanation

The key insight is that electric potential energy change depends on both the charge and the potential difference—but the potential difference is the same for both particles since they travel between the same two points. So the ratio of their energy changes is simply the ratio of their charges. Notice that charge is signed: the positive charge gains energy moving to higher potential, while the negative charge loses it, giving opposite signs to their changes.

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