Question

A point charge of −3.50 µc is located in the center of a spherical cavity of radius 5.00 cm inside an insulating charged solid. the charge density in the solid is ρ = 7.35 × x10−4 c/m3 . calculate the electric field inside the solid at a distance of 10 cm from the center of the cavity.

Answer 1

As per Gauss law

`\int E. dA = (q)/(epsilon_0)`

here

q = total charge inside the gaussian surface

now in order to find q

`q = q_1 + \rho* (4)/(3)\pi(R^3 - a^3)`

`q = -3.50 \mu C + 7.35 * 10^(-4)* (4)/(3)\pi(0.10^3 - 0.05^3)`

`q = -2.86\mu C`

now electric field is given by

`E* 4\pi *0.10^2 = (-2.86 \muC)/(\epsilon_0)`

`E = (9*10^9*2.86*10^(-6))/(0.10^2)`

`E = 2.57 * 10^6 N/C`