Two nonconducting plates A and B of radii 2R and 4R, respectively, are kept at distances x and 2x from the point charge q. A surface cutout of a nonconducting shell C is kept such that its center coincides with the point charge. Each plate and spherical surface carries surface charge density σ.If FA, FB, and FC are the forces on plate A, plate B, and spherical surface C due to charge q, respectively, thenIf ϕ1 is flux through surface of (B) due to electric field of (A) and ϕ2 is the flux through (A) due to electric field of (B), thenIf distance x and radius R are doubled so that FA becomes FA′, FB becomes FB′, then the correct option is

For A and B we know that Flux=ϕ=∫E⋅ds Force =∫σE⋅ds=σ∫E⋅ds=σϕAs flux due to charge q in each plate is same, so force will be same.For C we have taken the horizontal component of electric field, but for flux, we do not have to take the component of electric field.As force due to one plate on another plate is same, hence ϕ due to 1 in another and due to 2 in 1 will be same.When x and R increased, ϕ in plate due to charge remains same, hence force due to charge on plates does not change.For A and B we know that Flu x=ϕ=∫E⋅ds Force =∫σE⋅ds=σ∫E⋅ds=σϕAs flux due to charge q in each plate is same, so force will be same.For C we have taken the horizontal component of electric field, but for flux, we do not have to take the component of electric field.As force due to one plate on another plate is same, hence ϕ due to 1 in another and due to 2 in 1 will be same.When x and R increased, ϕ in plate due to charge remains same, hence force due to charge on plates does not change.For A and B we know that Flu x=ϕ=∫E⋅ds Force =∫σE⋅ds=σ∫E⋅ds=σϕAs flux due to charge q in each plate is same, so force will be same.For C we have taken the horizontal component of electric field, but for flux, we do not have to take the component of electric field.As force due to one plate on another plate is same, hence ϕ due to 1 in another and due to 2 in 1 will be same.When x and R increased, ϕ in plate due to charge remains same, hence force due to charge on plates does not change.