Given:
Three-point charges are placed at the three corners of the square of side l.
The charges are respectively,
[tex]-2Q,\text{ Q, +3Q}[/tex]
To find:
The potential at the fourth corner
Explanation:
The distance between the opposite corners is,
[tex]\sqrt{2}l[/tex]
The potential at any point at a distance r, from a charge q is,
[tex]\begin{gathered} V=\frac{kq}{r} \\ k=9\times10^9\text{ N.m}^2.C^{-2} \end{gathered}[/tex]
For the charges in the three corners, the potential at the fourth corner is,
[tex]\begin{gathered} V=k[\frac{-2Q}{l}+\frac{Q}{\sqrt{2}l}+\frac{3Q}{l}] \\ =k\frac{-2\sqrt{2}Q+Q+3\sqrt{2}Q}{\sqrt{2}l} \\ =kQ\frac{1+\sqrt{2}}{\sqrt{2}l} \end{gathered}[/tex]
Hence, the potential at the fourth corner is,
[tex]kQ\frac{1+\sqrt{2}}{\sqrt{2}l}[/tex]
