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Consider two statements. Statement I: An electric dipole is placed at the centre of a hollow sphere. The net electric flux through the sphere is zero, yet the electric field is nonzero everywhere on/in the sphere. Statement II: A solid metal sphere of radius R carries total charge Q. At any point on a spherical Gaussian surface of radius r (< R), the electric field is zero, but the electric flux through that closed surface is not zero. Choose the correct option.

1. Both Statement I and Statement II are true.
2. Statement I is true but Statement II is false.
3. Both Statement I and Statement II are false.
4. Statement I is false but Statement II is true.

Correct answer: Statement I is true but Statement II is false.

Solution

Statement I: A dipole has zero net charge, so by Gauss's law the net flux through the enclosing sphere is zero; yet the dipole produces a nonzero field everywhere. Statement I is TRUE. Statement II: In a solid metallic sphere all the charge lies on the outer surface (radius R). A Gaussian sphere of radius r < R encloses zero charge, so both the field inside the metal is zero AND the flux through that surface is zero (not nonzero). The claim that the flux is nonzero is wrong. So Statement II is FALSE. Correct option: I true, II false.

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