two point charges + q and + 4 q are separated by a distance 6a find the point joining the two charges where the electric field is zero
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The electric fiels is zero at P only , if the field due to +Q+Q balance the field due to +4Q+4Q
14π∈0.Qx2=14π∈0.4q(6a−x)214π∈0.Qx2=14π∈0.4q(6a−x)2
1x2=4(6a−x)21x2=4(6a−x)2
Taking square root or both sides.
1x=2(6a−x)1x=2(6a−x)
On cross multiplying we get,
2x=6a−x2x=6a−x
x=2ax=2a
Hence the required point is at a distance of 2a2a from Q
14π∈0.Qx2=14π∈0.4q(6a−x)214π∈0.Qx2=14π∈0.4q(6a−x)2
1x2=4(6a−x)21x2=4(6a−x)2
Taking square root or both sides.
1x=2(6a−x)1x=2(6a−x)
On cross multiplying we get,
2x=6a−x2x=6a−x
x=2ax=2a
Hence the required point is at a distance of 2a2a from Q
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