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 :

Engineering

Physics

Electric Potential Energy and Electric Potential

Question

$\frac{Q ℓn 2}{4 {πε}_{0} L}$

$\frac{Q}{8 {πε}_{0} L}$

$\frac{3 Q}{4 {πε}_{0} L}$

$\frac{Q}{4 {πε}_{0} Lln 2}$

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$V = \int_{0}^{L} k \frac{Q}{L} \frac{dx}{(L + x)}$

$= \frac{kQ}{L} {[ℓn (L + x)]}_{0}^{L}$

$= \frac{kQ}{L} ℓn \frac{2 L}{2 L} = \frac{{kQℓn}^{2}}{L}$

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