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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

`-4`

B

`-32/25`

C

`32/25`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`q_(1)=rho_(1)4/3 pi R^(3), q_(2)=rho_(2)4/3 pi (2R)^(3)`

if `E_("net")=0` at point A then
`(kq_(1))/((2R)^(2))+(kq_(2))/((5R)^(2))=0 rArr q_(1)/q_(2)=-4/25rArr rho_(1)/rho_(2)=-32/25`
if `E_("net")=0` at point B then
`(kq_(1))/((2R)^(2))=(kq_(2)R)/((2R)^(3))rArr q_(1)/q_(2)=1/2rArr rho_(1)/rho_(2)=4`
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