Question

Charges $1\mu C$ are placed at each of the four corners of a square of side $2\sqrt{2}m$. The potential at the point of intersection of the diagonals is _____ $(K=9\times {10}^{9}SIunit)$.

• A. $18\times {10}^{3}V$
• B. $1800V$
• C. $18\sqrt{2}\times {10}^{3}V$
• D. None of these

Answer 1

The correct option is A $18\times {10}^{3}V$

Key Concept Here, we have to find the electric potential due to multiple of charges, so, we have to apply superposition principle to calculate net electric potential.
Length of the diagonals $=\sqrt{2}\times$ side length
$=\sqrt{2}\times 2\sqrt{2}=4m$
$\therefore$ Length of semi-diagonals $=\frac{4}{2}=2m$.
Now, potential due to charges at point $O$
$V_0=\frac{!}{4\pi {ϵ}_0}\left(\frac{1\times {10}^{-6}}{2}\right)\times 4$
$=9\times {10}^9\times {10}^{-6}\times 2=18\times {10}^{3}V$.