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Electric Potential & Equipotentials question from JEE Main 2013

Q113JEE Main 2013Medium

Electric Potential & Equipotentials

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 distance $L$ from the end $A$ is

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Answer: (d)

Take $O$ as origin; the rod runs from $x = L$ to $x = 2L$ with $\lambda = Q/L$ .
$V = \displaystyle\int_L^{2L} \dfrac{k\lambda\,dx}{x} = k\lambda\ln 2$
$V = \dfrac{Q\ln 2}{4\pi\varepsilon_0 L}$
So the answer is (d).

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