Question

A thin dielectric rod of length $l$ lies along X-axis. One end is at the origin and the other at ($l$, 0). A total charge Q is distributed uniformly. What is the potential at point (x, 0) when $x > l$?

• A. $\fracQ4π\epsilon₀ l \logₑ \left(\fracxx-l\right)$
• B. $\fracQ4π\epsilon₀ l \logₑ \left(\fracxl\right)$
• C. $\fracQ4π\epsilon₀ l \logₑ \left(\fracx-lx\right)$
• D. $\fracQ4π\epsilon₀ l}$

Hint:

Potential due to continuous charge distribution: $V = \int \fracdq4π\epsilon₀ r}$.

Answer 1

The Correct Option is A

Step 1: $λ = Q/l$. $V = \int₀l \fracλ dz4π\epsilon₀ (x-z)}$.

Step 2: $V = \fracQ4π\epsilon₀ l [-\ln(x-z)]₀l = \fracQ4π\epsilon₀ l \ln\left(\fracxx-l\right)$.