Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii `R//2`, R and 2R respectively, as shown in figure. If magnitude of the electric fields at point P at a distance R from the centre of sphere 1,2 and 3 are `E_1, E_2 and E_3` respectively, then

Options

A. `E_1 gt E_2 gt E_3`
B. `E_3 gt E_1 gt E_2`
C. `E_2 gt E_1 gt E_3`
D. `E_3 gt E_2 gt E_1`

Answer

C

Explanation

`E_1=1/(4piepsilon_0)Q/R^2`…(i)
`E_2=1/(4piepsilon_0)(2Q)/R^2`….(ii)
Now for the third sphere , we can calculate the volume charge density `(rho)` so that we may use `E=(rho x)/(3epsilon_0)` to calculate `E_3` . Here x is the distance of point from the centre of sphere and x=R in this case .
`rho=(4Q)/(4/3 pi(2R)^3)=(3Q)/(8piR^3)` .....(iii)
`E_3=("3Q"/(8piR^3)R)/(3epsilon_0)`
`E_3=Q/(8piepsilon_0R^2)`....(iv)
From equation (i),(ii) and (iii), we can see that : `E_2 > E_1 > E_3`