Question

Two spherical cavities of radii a and b are hollowed out from the interior of a netural conducting sphere of radius R. At the center of each cavity, a point charge is placed. Call these charges $q_a$ and $q_b$ The electric field inside the cavity of radius a at a distance r from the center of cavity is

• A. $\frac{1}{4\pi {\epsilon }_0}\frac{q_a}{r^2}$
• B. $-\frac{1}{4\pi {\epsilon }_0}\frac{q_a}{r^2}$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{q_a+q_b}{r^2}$
• D. zero

Answer 1

The correct option is A $\frac{1}{4\pi {\epsilon }_0}\frac{q_a}{r^2}$

Consider a Gaussian sphere of radius r inside the cavity of radius a. Using Gauss's law the electric field inside the cavity: $E.4\pi r^2=\frac{Q_{enclosed}}{{ϵ}_0}=\frac{q_a}{{ϵ}_0}$
$\therefore E=\frac{1}{4\pi {ϵ}_0}\frac{q_a}{r^2}$