Question

At each of the four corners of a square of side a,a charge +q is placed freely.whar charge should be placed at the centre of the square

Answer 1





The given system consist 4 point charges +q placed at 4 corners A, B, C and D of  a square of side a and a charge Q at the centre of the square. Any system of charges is in equilibrium if its total electric potential energy is equal to zero.

Hence, Usystem=PE due to all those pairs in which charges placed at the corners of the sidesof square+PE due to all those pairs in which charges are placed at the ends of diagonal of square+PE due to pairs formed by any charge at the corner and charge at the centre.Usystem=4×14πε0×q2a+2×14πε0×q2a√2+4××14πε0×qQa/√2Usystem=14πε0×4qa[q+q2√2+Q√2]The system will be in equilibrium ifUsystem=014πε0×4qa[q+q2√2+Q√2]=0q+q2√2+Q√2=0Q√2=−(q+q2√2)Q=−(q√2+q4)Q=−q(2√2+14)Q=−q4(2√2+1)

Answer 2

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