Question

The electrostatic potential on the surface of a charged conducting sphere is $100V$. 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 $100V$.
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
$E=-\frac{dV}{dr}$
Electric field intensity $E=0$ suggest that
$\frac{dV}{dr}=0$
This imply that $V=$ constant.
Thus, $E=0$ inside the charged conducting sphere causes the same electrostatic potential $100V$ at any point inside the sphere.