Ncert Exercises & Solutions

Refer to the arrangement of charges in the figure and a Gaussian surface of a radius $R$ with $Q$ at the centre. Then:

(a)	total flux through the surface of the sphere is $\frac{-Q}{\varepsilon_0}.$
(b)	field on the surface of the sphere is $\frac{-Q}{4\pi \varepsilon_0 R^2}.$
(c)	flux through the surface of the sphere due to $5Q$ is zero.
(d)	field on the surface of the sphere due to $-2Q$ is the same everywhere.

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.

Step 1: Find the net flux passing through the surface.

Gauss' law states that the total electric flux of an enclosed surface is given by

\frac{q}{ϵ_{0}}

$\frac{q}{\epsilon_0}$ where

q

$q$ is the charge enclosed by the surface. Thus, from the figure,

The total charge inside the surface is

= Q - 2 Q = - Q

$= Q - 2Q = -Q$
The total flux through the surface of the sphere

= - \frac{Q}{ϵ_{0}}

$=-\frac{Q}{\epsilon_0}$

Step 2: Find the flux due to the

5 Q

$5Q$ charge.

Now, consider the charge

5 Q .

$5Q.$
The charge

5 Q

$5Q$ lies outside the surface, thus it makes no contribution to electric flux through the given surface.
Therefore, the flux through the surface of the sphere due to

5 Q

$5Q$ is zero.
Hence, option (2) is the correct answer.

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