Two nonconducting plates A and B of radii 2R and 4R, respectively, are kept at distance x and 2x from the point charge q. A surface cutout of a nonconducting shell A is kept such that is center coincides with the point charge. Each plate and spherical surface carries surface charge density `sigma`.

If distance x and radius R are doubled so that `F_A` becomes `F'A,F_B becomes F'B`, then the correct option is

Options

A. `F_BgtF'_B`
B. `F'_BgtF_B`
C. `F'_AgtF'_B`
D. none of these

Answer

D

Explanation

For A and B we know that
Flux `=phi=intE.ds`
Force `=intsigmaE.ds=sigmaintE.ds=sigmaphi`
As flux due to charge q in each plate is same force will be same. For C we have taken the horizontal component of electric field , but for As force due to one plate on another plate is same, hence `phi` due to 1 in another and due to 2 in 1 will be same. When x and R increased `phi` in plate due to charge remains same, hence force due to charge on plates does not change.