Question

Calculate the electric potential at point A where x = - d.

Answer 1

Electric potential at point A due to infinitely small element $dx$ of rod at x is :
$dPE=\frac{1}{4\pi ϵ}\frac{axdx}{x+d}$
total PE at point A = ${\int }_0^L\frac{1}{4\pi ϵ}\frac{axdx}{x+d}=\frac{a}{4\pi ϵ}{\int }_0^{L}1-\frac{d}{x+d}dx=\frac{a}{4\pi ϵ}[L-dln(\frac{d+L}{d}\left)\right]$