A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric…

1. $\frac{\text{Q}}{4\pi {\in }_0\text{L}\mathit{\text{ ln }}2}$
2. $\frac{\text{Q}\mathit{\text{ ln }}2}{4\pi {\in }_0\text{L}}$
3. $\frac{\text{Q}}{8\pi {\in }_0\text{L}}$
4. $\frac{3\text{Q}}{4\pi {\in }_0\text{L}}$

Solution

$\text{V}=\underset{\text{L}}{\overset{2\text{L}}{\int }}\frac{\text{kdq}}{\text{x}}$

$=\underset{\text{L}}{\overset{2\text{L}}{\int }}\frac{1}{4\pi {\epsilon }_0}\frac{\left(\frac{\text{Q}}{\text{L}}\right)\text{dx}}{\text{x}}$

$=\frac{\text{Q}}{4\pi {\epsilon }_0\text{L}}\ell \text{n}\left(2\right)$

Asked in: JEE Main 2013 (07 Apr)

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