Question

Four Charges $1\times {10}^{-8}C,-2\times {10}^{-8}C,3\times {10}^{-8},3\times {10}^{-8}$ are placed at the four corners of a square of side 1 m. The potential at the centre of the square is

• A. $450V$
• B. $450\sqrt{2}V$
• C. $180V$
• D. $180\sqrt{2}V$

Answer 1

The correct option is B $450\sqrt{2}V$

$V=V_1+V_2+V_3+V_4=\frac{1}{4\pi {ϵ}_0}\frac{1}{r}[q_1+q_2+q_3+q_4]=9\times {10}^9\times \frac{1}{\frac{1}{\sqrt{2}}}[1-2+3+3]\times {10}^{-8}=9\times 10\times \sqrt{2}\times 5=450\sqrt{2}V$