Question

Following figure shows for Gaussian surface $S_1,S_2,S_3$ and $S_4$.

Now, match the following columns and mark the correct code given below.

Column I		Column II
i	${\varphi }_{S_1}$	p	$+\frac{Q}{{\epsilon }_0}$
ii	${\varphi }_{S_2}$	q	0
iii	${\varphi }_{S_3}$	r	$-\frac{Q}{{\epsilon }_0}$
iv	${\varphi }_{S_4}$	s	$-\frac{2Q}{{\epsilon }_0}$

• A. i- (s) , ii - (q) , iii - (r) , iv - (p)
• B. i - (q), ii - (s), iii - (r), iv - (p)
• C. i - (q), ii - (r), iii - (s), iv - (p)
• D. i - (r) , ii - (s) , iii - (p) , iv - (q)

Answer 1

Answer: (A)

The net flux through each closed surface is determined by the net charge inside. ${\varphi }_{s_1}=\frac{(+Q-3Q)}{{\epsilon }_0}=\frac{-2Q}{{\epsilon }_0}$
${\varphi }_{s_2}=\frac{(+Q+2Q-3Q)}{{\epsilon }_0}=0$
${\varphi }_{s_3}=\frac{(+2Q-3Q)}{{\epsilon }_0}=-\frac{Q}{{\epsilon }_0}$
${\varphi }_{s_4}=+\frac{Q}{{\epsilon }_0}$