A solid spherical region having a spherical cavity whose daimeter `R` is equal to the radius of the spherical region, has a total charge `'Q'`. Find the electric field and potential at a point `P` as shown.

Explanation

Charge density `rho=(Q)/((4)/(3)pi[R^(3)-((R)/(2))^(3)])=(6Q)/(7piR^(3))`
Using the superposition principle,
`V=(rho[(4)/(3)piR^(3)])/(4piepsilon_(0)x)-(rho[(4)/(3)pi((R)/(2))^(3)])/(4piepsilon_(0)[x-(R )/(2)])=(rhoR^(3))/(3epsilon_(0))([7x-4R])/(4x(2x-R))`
Similarly,
`E=(rho[(4)/(3)piR^(3)])/(4piepsilon_(0)x^(2))-(rho[(4)/(3)pi((R)/(2))^(3)])/(4piepsilon_(0)[x-(R )/(2)])=(rhoR^(3))/(3epsilon_(0))[(1)/(x^(2))-(1)/(2(2x-R)^(2))]`