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Question

# Two spherical, non conducting, and very thin shells of uniformly distributed positive charge Q and radius d are located a distance 10d from each other. A positive point charge q is placed inside one of the shells at a distance d/2 from the center, on the line connecting the centers of the two shells, as show in the figure. What is the net force on the charge q?

A
Qq361πε0d2 to the left
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B
Qq361πε0d2 to the right
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C
362Qq361πε0d2 to the left
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D
360Qq361πε0d2 to the right
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Solution

## The correct option is A Qq361πε0d2 to the left The charge is inside one of the shells. The electric field due to this shell inside is zero, so no force would act on it due to this shell. The only force experienced by the charge would be due to the electric field due to the shell which is at the distance. Thus we get E=kQr2 where, r=10d−d2=19d2 Therefore, E=kQ(19d2)2 E=4kQ361d2 E=Q361πϵ0d2 Now, considering the force exerted by opposite sphere to the left, we can write F=qE=qQ361πϵ0d2

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