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Two non-conducting solid spheres of radi...

Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities `rho_1` and `rho_2` respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio `rho_1/rho_2` can be

A

(a) `-4`

B

(b) `-33/25`

C

(c) `32/25`

D

(d) 4

Text Solution

Verified by Experts

The correct Answer is:
D
Electric field `E_1` due to smaller sphere at P is

`E_1=(1)/(4pi in_0)xx(rho_1piR)/(3)=(rho_1R)/(4 in_0xx3)`
Electric field `E_2` due to bigger sphere at P is
`E_2=(rho_2R)/(3in_0)`
As `E_1=E_2` `:.` `(rho_1R)/(4 in_0xx3)=(rho_2R)/(3 in_0)implies(rho_1)/(rho_2)=4`
Option (d) is correct.
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