Four identical charges $ + \,50\,\mu C$ each are placed, one at each corner of a square of side $2\,m$. How much external energy is required to bring another charge of $ + \,50\,\mu C$ from infinity to the centre of the square......$J$ $\left( {{\rm{Given}}\frac{{\rm{1}}}{{{\rm{4}}\pi {\varepsilon _{\rm{0}}}}} = 9 \times {{10}^9}\,\frac{{N{m^2}}}{{{C^2}}}} \right)$
Medium
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(a) Potential at the centre of square
$V = 4\, \times \,\left( {\frac{{9 \times {{10}^9} \times 50 \times {{10}^{ - 6}}}}{{2/\sqrt 2 }}} \right) = 90\sqrt 2 \times {10^4}\,V$
Work done in bringing a charge $(q = 50\, \mu C)$ from $\infty$ to centre $(O)$ of the square is $W = q\,({V_0} - {V_\infty }) = q{V_0}$ $==>$
$W = 50 \times {10^{ - 6}} \times 90\sqrt 2 \times {10^4} = 64\,J$
$V = 4\, \times \,\left( {\frac{{9 \times {{10}^9} \times 50 \times {{10}^{ - 6}}}}{{2/\sqrt 2 }}} \right) = 90\sqrt 2 \times {10^4}\,V$
Work done in bringing a charge $(q = 50\, \mu C)$ from $\infty$ to centre $(O)$ of the square is $W = q\,({V_0} - {V_\infty }) = q{V_0}$ $==>$
$W = 50 \times {10^{ - 6}} \times 90\sqrt 2 \times {10^4} = 64\,J$
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