Given below are two statements:
Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.
Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero..
In the light of the above statements, choose the correct answer from the options given below :

Solution

Physics sir · 3 steps

Flux sees only the enclosed charge, but the field feels every charge nearby.

1. Statement I. The dipole has +q and -q inside the sphere, so q_(enc) = 0 and the flux q_(enc)/ε₀ is zero. The two charges still produce a field at every point, because their fields do not cancel exactly anywhere. Statement I is true.

   ∮ E⃗· dA⃗ = q_(enc)/ε₀

2. Statement II. In a conductor, all of the charge Q sits on the outer surface at radius R. A sphere of radius r < R encloses no charge, so the flux through it is zero. The field inside the metal is also zero. Statement II claims the flux is not zero, so it is false.
3. So. Statement I is true and Statement II is false, which is option (c).

The idea to keep. Gauss's law fixes the flux from the enclosed charge alone. Zero flux can come with a nonzero field (a dipole inside), and inside a conductor both the field and the flux are zero.

Answer from the NTA final answer key. Solution by PrepWiser.