Question

Find the potential at the centre of a square of side $ \sqrt{2}m $ . Which carries at its four comers charges $ {{q}_{1}}=3\times {{10}^{-6}}C,{{q}_{2}}=-3\times {{10}^{-6}}C, $ $ {{q}_{3}}=-4\times {{10}^{-6}}C,{{q}_{4}}=7\times {{10}^{-6}}C $

• A. $ 2.7\times {{10}^{4}}V $
• B. $ 1.5\times {{10}^{3}}V $
• C. $ 3\times {{10}^{2}}V $
• D. $ 5\times {{10}^{3}}V $
• E. $ 3\times {{10}^{3}}V $

Answer 1

Answer: (A)

The potential $ V=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{1}{r}({{q}_{1}}+{{q}_{2}}+{{q}_{3}}+{{q}_{4}}) $
$ V=(9\times {{10}^{9}})\left( \frac{1}{1m} \right)\{(3-3-4+7)\times {{10}^{-6}}C\} $
$ =2.7\times {{10}^{4}}\frac{N-m}{C}=2.7\times {{10}^{4}}\frac{J}{C} $
$ =2.7\times {{10}^{4}}V $