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A neutral conducting sphere of radius R has a spherical cavity of radius R/4 whose centre is located at a distance R/2 from the centre of the sphere. No charge is placed inside the cavity. Which of the following statements about the electric field is correct?

1. (A) The electric field inside the cavity is zero everywhere
2. (B) The electric field just outside the outer surface of the conductor is zero
3. (C) The electric field inside the conductor (in the bulk material) is non-zero
4. (D) The net charge induced on the inner cavity wall is non-zero

Correct answer: (A) The electric field inside the cavity is zero everywhere

Solution

For a neutral conductor with an empty cavity, all charge resides on the outer surface. The electric field inside the conducting material is zero (conductor property). Since no charge is inside the cavity, by Gauss's law and uniqueness theorem, E = 0 inside the cavity as well. No charge is induced on the inner cavity wall.

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