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Question

A positive charge q is placed in front of a conducting solid cube of side a at distance d from its center. Find the electric field at the center of the cube due to the charges appearing on its surface.


A
Zero
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B
Kqd2
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C
Kq4d2
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D
2Kqd2
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Solution

The correct option is B Kqd2
Since field inside a conductor is always zero.i.e., Econductor=0

Hence, field due to charge q and those appearing at surface should cancel each other.

So, we have
Econductor=Esurface charge+Eq=0.....(1)

Where,
Esurface charge=Electric field at the centre of conductore due the charges appearing on the surface.

Eq=Kqd2=Electric field due the point charge at the centre of the conductor.

From equation (1), we get
Esurface charge=Eq=Kqd2

Hence, the magnitude of field at center due to charges appearing at surfaces is Kqd2, directed towards the charge q.

Thus, option (b) is the correct answer.

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