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Question:

For equal point charges Q each are placed in the xy plane at (0,2), (4,2),(4,-2) and (0,-2). The work required to put a fifth Q at the origin of the coordinate system will be:

Q²/(2√2πε₀)

Q²/(4πε₀)(1+1/√5)

Q²/(4πε₀)(1+1/√3)

Q²/(4πε₀)

Solution:

The correct option is B
Q²/(4πε₀)(1+1/√5)
potential at origin =kQ/2+kQ/2+kQ/√20+kQ/√20 (potential at ∞=0)=kQ(1+1/√5)
work required to put a fifth charge Q at origin is equal to Q²/(4πε₀)(1+1/√5)