Charge is distributed uniformly on the surface of a spherical nonconducting shell.A point particle with charge q is inside.The electrical force on the particle q is least when:

Question

Quizplus · Accepted Answer

The electrical force on the point particle q is given by Coulomb's law:
$$
\vec{F}=\frac{1}{4\pi\epsilon_0}\frac{qQ}{r^2}\hat{r}
$$
where $\vec{r}$ is the vector pointing from the center of the shell to the point particle, $Q$ is the total charge on the shell, and $\epsilon_0$ is the electric constant. Since the charge is distributed uniformly on the surface of the shell, we can write $Q=\sigma A$, where $\sigma$ is the surface charge density and $A$ is the surface area of the shell. Hence,
$$
\vec{F}=\frac{1}{4\pi\epsilon_0}\frac{q\sigma A}{r^2}\frac{\vec{r}}{r}.
$$
Since the charge is distributed uniformly on the shell, the electric field at any point inside the shell is zero. Therefore, the electric force on the particle is also zero everywhere inside the shell. Thus, the answer is E, and the force is zero everywhere inside.

Charge Is Distributed Uniformly on the Surface of a Spherical