Four electric charges +q,+q,−q and −q are placed at the corners of a square of side 2L (see figure). The electric potential at point A, midway between the two charges +q and +q, is
14πϵ02qL(1+√5)
14πϵ02qL(1+1√5)
14πϵ02qL(1−1√5)
zero
A
14πϵ02qL(1−1√5)
B
14πϵ02qL(1+1√5)
C
14πϵ02qL(1+√5)
D
zero
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Solution
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Here, AB=AE=L and
AC=AD=√AB2+BC2=√L2+(2L)2=√5L
Potential at A is
VA=14πϵ0[qAB+−qAC+−qAD+qAE]
or VA=14πϵ0[qL+−q√5L+−q√5L+qL]=14πϵ02qL[1−1√5]
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