Question

The potential energy $U(r)$ of two point charges at a distance of $r$ is proportional to

• A. $-\frac{1}{r}$
• B. $\frac{1}{r^2}$
• C. $\frac{1}{r^3}$
• D. $\frac{1}{r}$

Hint:

In electrostatics: - Force varies as $\frac{1}{r^2}$, - Potential and potential energy vary as $\frac{1}{r}$.

Answer 1

The Correct Option is D

Concept: The electrostatic potential energy between two point charges is given by Coulomb’s law: \[ U(r) = \frac{1}{4\pi \epsilon_0} \cdot \frac{q_1 q_2}{r} \] This shows that the potential energy depends inversely on the distance between the charges.

Step 1: Write the expression for potential energy.
\[ U(r) = \frac{1}{4\pi \epsilon_0} \cdot \frac{q_1 q_2}{r} \]

Step 2: Identify proportionality.
From the formula, we observe: \[ U(r) \propto \frac{1}{r} \]

Step 3: Final conclusion.
Hence, the potential energy varies inversely with distance $r$, so the correct answer is: \[ \frac{1}{r} \]