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 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
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Conducting Sphere Rule: The electric potential anywhere inside is uniform and exactly equal to its value on the surface! No calculation needed.
Updated On: Jun 3, 2026
- 3 V
- 4 V
- 0 V
- 5 V
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The Correct Option is D
Solution and Explanation
Step 1: Concept
For any hollow or solid conducting body in static equilibrium, the electric field inside the interior volume is identically zero ($E = 0$).
Step 2: Meaning
Because the electric field is related to potential by $E = -\frac{dV}{dr}$, a zero electric field ($E = 0$) means that the change in potential is zero ($\frac{dV}{dr} = 0$). Thus, the electric potential remains constant at all points inside the conductor.
Step 3: Analysis
The radius of the conducting sphere is $R = 4 \text{ cm}$. A point located at a depth of 1 cm from its surface lies at a distance of $r = 4 - 1 = 3 \text{ cm}$ from the center. Since $r < R$, this point lies completely inside the body of the conductor. Consequently, its potential must match the potential at the surface.
Step 4: Conclusion
Since the surface potential is 5V, the potential inside at a depth of 1 cm is also exactly 5V.
Final Answer: (D)
For any hollow or solid conducting body in static equilibrium, the electric field inside the interior volume is identically zero ($E = 0$).
Step 2: Meaning
Because the electric field is related to potential by $E = -\frac{dV}{dr}$, a zero electric field ($E = 0$) means that the change in potential is zero ($\frac{dV}{dr} = 0$). Thus, the electric potential remains constant at all points inside the conductor.
Step 3: Analysis
The radius of the conducting sphere is $R = 4 \text{ cm}$. A point located at a depth of 1 cm from its surface lies at a distance of $r = 4 - 1 = 3 \text{ cm}$ from the center. Since $r < R$, this point lies completely inside the body of the conductor. Consequently, its potential must match the potential at the surface.
Step 4: Conclusion
Since the surface potential is 5V, the potential inside at a depth of 1 cm is also exactly 5V.
Final Answer: (D)
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