Question

A soild non conducting sphere of uniform charge distribution have a cavity with no charge such that both cavity and sphere are concentric. The radius of cavity is half the radius of sphere. Calculate electric field inside cavity

Answer 1

0

Answer 2

The electric field inside a uniformly charged solid sphere at a distance $\vec{x}$ from the center is $\vec{E}_{sphere} = \frac{\rho \vec{x}}{3\epsilon_0}$. A uniformly charged sphere with a concentric cavity can be considered as a complete sphere with charge density $\rho$ minus a sphere filling the cavity with charge density $-\rho$.

By superposition, the field inside the cavity is the field due to the large sphere (density $\rho$) plus the field due to the cavity-sized sphere (density $-\rho$). Since both hypothetical spheres are centered at the same point as the cavity, the field at point $\vec{x}$ inside the cavity due to the large sphere is $\frac{\rho \vec{x}}{3\epsilon_0}$, and the field due to the small sphere is $\frac{(-\rho) \vec{x}}{3\epsilon_0}$. The sum of these two fields is $\frac{\rho \vec{x}}{3\epsilon_0} - \frac{\rho \vec{x}}{3\epsilon_0} = \vec{0}$.