Given below are two statements: Statement \(I :\) An electric dipole is placed at the centre of a hollow sphere. The flux of 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:

A Both Statement \(I\) and Statement \(II\) are true
B Statement \(I\) is true but Statement \(II\) is false
C Both Statement \(I\) and Statement \(II\) are false
D Statement \(I\) is false but Statement \(II\) is true.

Verified Solution

Answer & Solution

Correct Answer

(B) Statement \(I\) is true but Statement \(II\) is false

Step-by-step Solution

Detailed explanation

\(\oint \vec{E} \cdot \overline{d s}=\frac{q_{i n}}{\varepsilon_{0}}=0=\phi\) Flux of \(\overrightarrow{ E }\) through sphere is zero. But \(\oint \overrightarrow{ E } \cdot \overline{ d s}=0 \Rightarrow\{\overrightarrow{ E } \cdot \overline{ d } \neq 0\}\) for small section…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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