Question

A radius of a spherical charged shell is 10 cm, and the electric potential on its surface is 100 V. Then, the potential at 2 cm from the center of the shell will be

Hint:

Inside a conducting charged spherical shell, the electric field is zero, and the potential remains constant throughout the interior.

Answer 1

Step 1: Understanding the Concept of a Spherical Shell 
According to Gauss's Law, the electric potential inside a charged conducting spherical shell is constant and equal to the potential on its surface. However, for an insulating spherical shell, the potential follows a different equation. 
Step 2: Given Data 
- Radius of the charged shell: \( R = 10 \) cm
- Potential on the surface: \( V_s = 100 \) V
- Distance from the center where potential is to be found: \( r = 2 \) cm 
Step 3: Applying the Concept 
For a conducting spherical shell, the potential inside the shell remains constant and is equal to the surface potential: \[ V_{{inside}} = V_{{surface}} \] Thus, at \( r = 2 \) cm (inside the shell), \[ V = V_{{surface}} = 100 { V} \] However, if the shell is non-conducting, then the potential at any point inside is given by: \[ V = \frac{kQ}{R} \] Since inside a conducting shell, the charge is distributed on the outer surface, the electric field inside is zero, leading to a constant potential. 
Step 4: Conclusion 
Since the given problem is based on a charged conducting spherical shell, the potential inside is constant. Thus, the potential at \( r = 2 \) cm from the center is: \[ V = 0 { V} \]