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# Four charges are arranged at the corners of a square ABCD of side d, as shown in Figure .A charge $q_0$ is brought to the centre E of the square, the four charges being held fixed at its corners. How much extra work is needed to do this?

The extra work necessary to bring a charge q0 to the point E when the four charges are at A, B, C and D is $q_0$ × (electrostatic potential at E due to the charges at A, B, C and D). The electrostatic potential at E is clearly zero since potential due to A and C is cancelled by that due to B and D. Hence no work is required to bring any charge to point E.