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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

At point `P_(1) = (1)/(4 pi epsilon_(0)) (rho_(1) (4//3)pi R^(3))/(4R^(2)) = (rho_(2)R)/(3 epsilon_(0))`

`(rho_(1) R)/(12) = (rho_(2) R)/(3)` or `(rho_(1))/(rho_(2)) = 4`
at point `P_(2)`
`(rho_(1)(4//3)piR^(2))/((2R)^(2)) + (rho(4//3)pi 8 R^(2))/((5R)^(2)) = 0`
or `(rho_(1))/(rho_(2)) = - (rho_(1))/(rho_(2)) = -(32)/(25)`
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