Two nonconducting 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 center of the spheres is zero. The ratio `rho_1//rho_2` can be

Options

A. `-4`
B. `-(32)/(25)`
C. `(32)/(25)`
D. `4`

Answer

A, B

Explanation

At point `P,(p_(1)R)/(3epsi_(0))=(p_(2)4/3piR^(3))/(4piepsi_(0)(2R)^(2))therefore(p_(1))/(p_(2))=4`
At point `theta`, if resultant electric field is zero,
then `(KQ_(1))/(4R^(2))+(KQ_(2))/(25R^(2))=0,(P_(1))/(P_(2))=-32/25(p_(1)` must be negative`)`