Question

A solid spherical region, having a spherical cavity whose diameter R is equal to the radius of the spherical region, has a total charge Q. Find the electric field at a point P as shown in figure
.

Answer 1

Correct Answer - `(Q)/(28 pi epsilon_(0)) [ (8)/( x^(2)) - (1)/((x -(R)/(2))^(2))]`
Volumetric charge density of given structure is
`rho = Q/(4/3piR^3 - 4/3pi(R/2)^3) = 8/7 Q/(4/3piR^3)`

`1Q_1 = rho 4/3 piR^3 = 8/7 Q, Q_2 = rho 4/3 pi (R/2)^3 = 1/7Q`
`E_(P) = E_1-E_2 = 1/(4piepsilon_0) Q_1/x^2 - 1/(4piepsilon_0) Q_2/(x-R/2)^2`
`= Q/(28piepsilon_0) [8/x^2 - 1/(x- R/2)^2]`.