A charge Q is uniformly distributed over a long rod AB of le... | Physics | SolveeIt

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 distance L from the end A is

$\frac{Q}{8 p \varepsilon_0 L}$

$\frac{3Q}{4 p \varepsilon_0 L}$

$\frac{Q}{4 p \varepsilon_0 L\, In\, 2}$

$\frac{Q\, In\, 2}{4 p \varepsilon_0 L}$

Answer

$\frac{Q\, In\, 2}{4 p \varepsilon_0 L}$

Explanation

Solution

$V=\int ^{2L}_L \frac{kdQ}{x}=\int ^{2L}_L \frac{k\bigg(\frac{Q}{L}\bigg)dx}{x}=\frac{Q}{4 p\varepsilon_0 L} \int ^{2L}_L \bigg(\frac{1}{x}\bigg)dx$
$\hspace15mm =\frac{Q}{4 p\varepsilon_0 L} [\log_e\, x]^{2L}_L$
$\hspace15mm =\frac{Q}{4 p\varepsilon_0 L} [\log_e\, 2L- \log_e L]=\frac{Q}{4 p\varepsilon_0 L} In\, (2)$

Physics Question on electrostatic potential and capacitance

Solution