Ncert Exercises & Solutions

If there were only one type of charge in the universe, then:

(a)	$\oint_s {E} . {dS} \neq 0$ on any surface
(b)	$\oint_s {E} . {dS} = 0$ if the charge is outside the surface.
(c)	$\oint_s {E} . {dS}$ could not be defined.
(d)	$\oint_s {E} . {dS}=\frac{q}{\epsilon_0}$ if charges of magnitude $q$ were inside the surface.

Choose the correct statement(s):

1.	(a) and (d)	2.	(a) and (c)
3.	(b) and (d)	4.	(c) and (d)

Hint: Use Gauss' law.

Explanation: The Gauss' law states that

\oint_{s} E . d S = \frac{q}{ϵ_{0}}

$\oint_s {E} . {dS}=\frac{q}{\epsilon_0}$ where

q

$q$ is the charge enclosed by the surface. If the charge is outside the surface, then the charge enclosed by the surface is equal to

0

$0$ and thus,

\oint_{s} E . d S = 0.

$\oint_s {E} . {dS} = 0.$ Here, the electric flux doesn't depend on the type or nature of the charge.
Hence, option (3) is the correct answer.