Electric charges of $ + 10\,\mu C,\; + 5\,\mu C,\; - 3\,\mu C$ and $ + 8\,\mu C$ are placed at the corners of a square of side $\sqrt 2 \,m$. the potential at the centre of the square is
Medium
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(c) Length of each side of square is $\sqrt 2 \,m$ so distance of it’s centre from each corner is $\frac{{\sqrt 2 }}{{\sqrt 2 }} = 1\,m.$
Potential at the centre
$V = 9 \times {10^9}\left[ {\frac{{10\, \times {{10}^{ - 6}}}}{1} + \frac{{5 \times {{10}^{ - 6}}}}{1} - \frac{{3 \times {{10}^{ - 6}}}}{1} + \frac{{8 \times {{10}^{ - 6}}}}{1}} \right]$
$= 1.8 \times 10^5 \,V$
Potential at the centre
$V = 9 \times {10^9}\left[ {\frac{{10\, \times {{10}^{ - 6}}}}{1} + \frac{{5 \times {{10}^{ - 6}}}}{1} - \frac{{3 \times {{10}^{ - 6}}}}{1} + \frac{{8 \times {{10}^{ - 6}}}}{1}} \right]$
$= 1.8 \times 10^5 \,V$
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