Question

A charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at a distance $L$ from the end $A$ is:

• A. $\frac{3Q}{4\pi {\epsilon }_{0}L}$
• B. $\frac{Q}{4\pi {\epsilon }_{0}L\ln 2}$
• C. $\frac{Q\ln 2}{4\pi {\epsilon }_{0}L}$
• D. $\frac{Q}{8\pi {\epsilon }_{0}L}$

Answer 1

Answer: (C)

$\frac{Q\ln 2}{4\pi {\epsilon }_{0}L}$

$V={\int }_{x=L}^{x=2L}\frac{k}{x}\left(\frac{Q}{L}\right)dx=\frac{Q\ln 2}{4\pi {\epsilon }_{0}L}$