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

Answer 1

Answer:

the force we will feel is F

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 depicts that force is not dependent on the distance and the charge is kept from one of the plate. Therefore,  force F felt by the charge is same when it is placed at a distance d/2 and at a distance d/4 from one of the plate.