Question

A conducting sphere of radius 4 cm is charged such that it has a potential of 5V on its surface. Then the potential at a point which is at a depth of 1 cm from its surface is

• A. 3 V
• B. 4 V
• C. 0 V
• D. 5 V

Hint:

Conducting Sphere Rule: The electric potential anywhere inside is uniform and exactly equal to its value on the surface! No calculation needed.

Answer 1

The Correct Option is D

Step 1: Field inside a conductor.
Inside any charged conductor in steady state the electric field is zero. Charges sit only on the surface.

Step 2: What zero field means for potential.
Since $E = -\dfrac{dV}{dr}$, a zero field means the potential does not change. So the potential is the same everywhere inside.

Step 3: Find the point's distance.
Radius is $4$ cm, depth is $1$ cm, so the point is at $r = 4 - 1 = 3$ cm from the centre.

Step 4: Is the point inside?
Since $3$ cm $< 4$ cm, the point lies inside the conductor.

Step 5: Apply the constant-potential rule.
Inside, the potential equals the surface potential, which is given as $5$ V.

Step 6: State the answer.
So the potential at that inside point is $5$ V, which is option 4.
\[ \boxed{V = 5 \text{ V}} \]