Q. An electric charge $ {{10}^{-3}}\,\mu C $ is placed at the origin (0, 0) of X-Y coordinate system. Two points A and B are situated at $ (\sqrt{2},\sqrt{2}) $ and (2, 0) respectively. The potential difference between the points A and B will be
Jharkhand CECEJharkhand CECE 2008
Solution:
Potential at A due to charge at O
$ {{V}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}=\frac{({{10}^{-3}})}{OA} $
$ =\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{({{10}^{-3}})}{\sqrt{{{(\sqrt{2})}^{2}}}+{{(\sqrt{2})}^{2}}} $
$ =\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{10}^{-3}}}{2} $
Potential at B due to charge at O
$ {{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{({{10}^{-3}})}{OB} $
$ =\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{({{10}^{-3}})}{2} $
So, $ {{V}_{A}}-{{V}_{B}}=0 $
