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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

AI Generated Solution

To solve the problem, we need to find the ratio of the volume charge densities \( \rho_1 \) and \( \rho_2 \) of two non-conducting solid spheres of radii \( R \) and \( 2R \) respectively, given that the net electric field at a distance \( 2R \) from the center of the smaller sphere is zero. ### Step-by-step Solution: 1. **Identify the Electric Fields**: - The electric field \( E_1 \) due to the smaller sphere (radius \( R \)) at a distance \( 2R \) from its center can be calculated using the formula for the electric field outside a uniformly charged sphere: \[ E_1 = \frac{K Q_1}{(2R)^2} ...
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