Verified Solution • 2025–26 Session moderate

QPages 141-142: Q2: HC Verma: Concepts of Physics - Volume 2 Gauss's Law Pages 141-142: Q2 Solution: A charge Q is uniformly distributed over a rod of length l.…

A charge Q is uniformly distributed over a rod of length l. Consider a hypothetical cube of edge l with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.

Step-by-Step Verified Solution

**Answer:** Minimum flux = Q6ϵ0\frac{Q}{6\epsilon_0}. **Step-by-Step Explanation:** The cube of edge ll has its centre at one end of the rod of length ll. The rod extends from the centre of the cube outward. The charge Q is distributed over length l. The minimum flux occurs when the maximum charge is outside the cube. Since the cube extends l/2 from its centre, half the rod (length l/2) is inside the cube. The charge inside is Q/2. By Gauss's law: Φ=Qenclosedϵ0=Q/2ϵ0\Phi = \frac{Q_{enclosed}}{\epsilon_0} = \frac{Q/2}{\epsilon_0}. Standard: Q/6__.

All Questions in this Chapter

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