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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
`E_p =0`
` Phi(r_1 4/3pR^2)/(( 4 pe_0 (2R)^2)) = (r_2 R)/(3e_0)`
`Phi r_1/r_2 =4`

` E_P' =0`
` Phi ( r_1 4/3 p R^3)/(4 pe_0 (2 R)^2) = ( -r _2 4/3 P (2R))^3/(4 pe_0(5R)^2)`
`Phi r_1/r_2 =- (32)/(25)` .
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