Question

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the entre (O) of shell can be graphically represented as –

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is D

For 𝑟 ≤ 𝑅, 𝑉 = 𝐾𝑄/𝑅 , i.e., Constant everywhere inside.

For 𝑟 > 𝑅, 𝑉 = 𝐾𝑄/𝑟 , i.e., Decreases with r.

Answer 2

Electric Potential of a Spherical Shell 

Step 1: Electric Potential Inside the Shell

For a uniformly charged thin spherical shell of radius \( R \) and total charge \( Q \), the electric potential inside the shell (\( r < R \)) is constant and equal to the potential at the surface:

\( V = \frac{kQ}{R} \)

where \( k \) is Coulomb's constant. This means the potential does *not* change as you move from the center towards the surface.

Step 2: Electric Potential Outside the Shell

For points outside the shell (\( r > R \)), the electric potential is the same as that of a point charge located at the center of the shell:

\( V = \frac{kQ}{r} \)

The potential decreases as the distance \( r \) increases, following an inverse relationship.

Step 3: Graphical Representation

Based on the above analysis:

• For \( r < R \) (inside the shell), \( V \) is constant.
• For \( r > R \) (outside the shell), \( V \) decreases with increasing \( r \) as \( \frac{1}{r} \).

This corresponds to a graph that is constant for \( r < R \) and then decreases hyperbolically for \( r > R \).

Conclusion:

The correct graphical representation is Option (4).