Question

Consider two hollow concentric spheres, S₁ and S₂, enclosing charges 2Q and 4Q respectively as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux through the sphere S₁ change if a medium of dielectric constant 'εr' is introduced in the space inside S₁ in place of air ? Deduce the necessary expression

Answer 1

 

(i) Charge enclosed by sphere S₁ = 2Q

By Gauss law, electric flux through sphere S₁ is

`phi_1=(2Q)/in_0`

Charge enclosed by sphere S₂ = 2Q+4Q=6Q

`:.phi_2=(6Q)/in_0`

The ratio of the electric flux is

`phi_1/phi_2=((2Q)/in_0)/((6Q)/in_0)=2/6=1/3`

 (ii) For sphere S₁, the electric flux is 

`phi'=(2q)/in_r`

`:.(phi')/phi_1=in_0/in_r`

`=>phi'=phi_1.in_0/in_r`

∵ ε_r > ε₀

 `:.phi'

Therefore, the electric flux through the sphere S₁ decreases with the introduction of the dielectric inside it.