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This is a two-statement question. After reading the statements, select the option that most accurately describes them. A non-conducting solid sphere of radius R carries a uniform positive volume charge density ρ. Because of this charge distribution, the electric potential is finite at the centre, at the surface, and at points outside the sphere. Take the potential at infinity to be zero. Statement 1: If a charge q is moved from the centre of the sphere to its surface, the change in its potential energy is qρ/(3ε0). Statement 2: For a point inside the sphere at a distance r from the centre, where r < R, the electric field magnitude is ρr/(3ε0).

1. Statement 1 is correct and Statement 2 is correct, but Statement 2 does not explain Statement 1.
2. Statement 1 is correct and Statement 2 is incorrect.
3. Statement 1 is incorrect and Statement 2 is correct.
4. Statement 1 is correct and Statement 2 is correct, and Statement 2 correctly explains Statement 1.

Correct answer: Statement 1 is incorrect and Statement 2 is correct.

Solution

Statement 1 is incorrect because the change in potential energy when moving a charge from the center to the surface of the sphere does not equal qρ/(3ε0). However, Statement 2 is correct as it accurately describes the electric field inside the sphere, which is derived from the uniform charge distribution.

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