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Q.

Four identical positive point charge q are placed at the corner of a square plate of side ‘d’. Another point fixed charge q is placed at a distance ‘d/2’ from the centre of square as shown. Choose the correct options.

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a

Electrostatic potential energy of the system is 2kq2d1+22+423

b

Flux through the square plate is q2ε0

c

Flux through the square plate is q6ε0

d

Work done in moving a charge q0 from infinity to the centre of the square plate with charges q each at the vertices is   2(22+1)kqq0d

answer is A.

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Detailed Solution

Usys=4kq2d+2kq22d+8kq23d=2kq2d22+1+423​Potential at the centre​Vf=42kqd+2kqdWork done = q0Vf−Vi=222+1kqq0d​The flux of charge at corners of square is zero.​Imagine a cube of side d , with q at its center.ϕcube=qε0​⇒ϕface=q6ε0
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