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 = [tex]\frac{\sigma}{2 \times \epsilon_{o}}[/tex]
where, [tex]\sigma[/tex] = 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 = [tex]\frac{\sigma}{2 \times \epsilon_{o}} + \frac{\sigma}{2 \times \epsilon_{o}}[/tex]
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 = [tex]q \times \frac{\sigma}{2 \times \epsilon_{o}}[/tex]
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 [tex]\frac{d}{2}[/tex] and at a distance [tex]\frac{d}{4}[/tex] from one of the plate.
Thus, we can conclude that the force we will feel is F.
