Question

Two very large parallel sheets a distance d apart have their centers directly opposite each other. The sheets carry equal but opposite uniform surface charge densities. A point charge that is placed near the middle of the sheets a distance d/2 from each of them feels an electrical force F due to the sheets. If this charge is now moved closer to one of the sheets so that it is a distance d/4 from that sheet, what force will feel?
(A) F
(B) 4F
(C) 2F
(D) F/2
(E) F/4

Answer 1

Answer:

(A) F

Explanation:

See it in the pic.

Answer 2

Answer: Option (A) is the correct answer.

Explanation:

According to the Gauss law, electric field due to very large sheet of charge is as follows.

                    E = $\frac{\sigma}{2 \times \epsilon_{o}}$

where,     $\sigma$ = charge per unit area

Since, it is given that there are two sheets of equal and opposite charge. Therefore, electric field between the plates will be as follows.

                  E = $\frac{\sigma}{2 \times \epsilon_{o}} + \frac{\sigma}{2 \times \epsilon_{o}}$

Also, we know that relation between force and electric field is as follows.

                       F = qE

Hence, force felt by the charge present inside the plates will be as follows.

                    F = $q \times \frac{\sigma}{2 \times \epsilon_{o}}$

This shows that force is not dependent on the distance and the charge is kept from one of the plate. Therefore, we can say that the force F felt by the charge is same when it is placed at a distance $\frac{d}{2}$ and at a distance $\frac{d}{4}$ from one of the plate.

Thus, we can conclude that the force we will feel is F.