4 A sphere with radius $\mathbf{2}\mathbf{}\mathbf{\text{cm}}$ is placed at a location near a point charge. The sphere has a charge of $\mathbf{-}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathbf{\text{C}}$ spread uniformly over its surface. The electric field due to the point charge has a magnitude of $\mathbf{500}\mathbf{}\mathbf{\text{N/C}}$ at the center of the sphere. What is the magnitude of the force on the sphere due to the point charge?

The given data can be listed below,

• The radius of sphere is, $r=2\text{cm}$.
• The charge on the sphere is, $q=-8\times {10}^{-10}\text{C}$.
• The magnitude of electric field due to point charge is, $E=500\text{N/C}$.

All the charges are densely bonded together in a continuous charge distribution, meaning there is very little space between them.

However, because the system is so tightly coupled, the electric charge does not remain constant. It is evident that the distribution of individual charges is continuous, with just a little gap between them.

The magnitude of force on the sphere is given by,

$F=Eq$

Here, E is the electric field and q is the charge on the sphere.

Substitute all the values in the above,

$$\begin{gathered} F=\left(500N/C\right)\left(-8\times {10}^{-10}C\right) \\ =-4.0\times {10}^{-7}N \end{gathered}$$

Thus, the magnitude of the force on the sphere due to point charge is$=-4.0\times {10}^{-7}N$