Question

The electrostatic potential on the surface of a charged conducting sphere is $100\, V$. Two statements are made in this regard:
$S_{1}:$ At any point inside the sphere, electric field intensity is zero.
$S_{2}:$ At any point inside the sphere, the electrostatic potential is $100\, V$.
Which of the following is a correct statement?

• A. $S_{1}$ is true but $S_{2}$ is false
• B. Both $S _{1}$ and $S_{2}$ are false
• C. $S_{1}$ is true, $S_{2}$ is also true and $S_{1}$ is the cause of $S_{2}$
• D. $S_{1}$ is true, $S_{2}$ is also true but the statements are independent

Answer 1

Answer: (C)

The electric field intensity $E$ and electric potential $V$ are related as
$E=-\frac{d V}{d r}$
Electric field intensity $E=0$ suggest that
$\frac{d V}{d r}=0$
This imply that $V=$ constant.
Thus, $E=0$ inside the charged conducting sphere causes the same electrostatic potential $100\, V$ at any point inside the sphere.