Question

Statement 1: A charge is outside the Gaussian sphere of radius $R$. Then electric field on the surface of sphere is zero.
Statement 2: As ${\oint }^{}\overrightarrow{E}.\overrightarrow{ds}=\frac{q_{in}}{{\epsilon }_0}$, for the sphere $q_{in}$ is zero, so ${\oint }^{}\overrightarrow{E}.\overrightarrow{ds}=0$

• A. Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement 1
• B. Statement 1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement 1
• C. Statement 1 is true, statement 2 is false
• D. Statement 1 is false, statement 2 is true

Answer 1

The correct option is A Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement 1

Statement 1 is true. Since the gaussian surface encloses no charge, so charge enclosed is zero.

From gauss' theorem, $\oint \overrightarrow{E}.\overrightarrow{dS}=\frac{Q_{enclosed}}{{\epsilon }_0}=0$

So, $\oint \overrightarrow{E}.\overrightarrow{dS}=0$

$\Rightarrow \overrightarrow{E}=0$

So, statement 2 gives correct explanation for statement 1.