Ncert Exercises & Solutions

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

(a)	total flux through the surface of the sphere is \(\dfrac{-Q}{\varepsilon_0}\).
(b)	field on the surface of the sphere is \(\dfrac{-Q}{4\pi \varepsilon_0 R^2}.\)
(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)

(2) 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}}

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

Total charge inside the surface is = Q - 2Q = -Q

∴

Total flux through the surface of the sphere

= \frac{- Q}{ε_{0}}

Step 2: Find the flux due to the 5Q charge.

Now, considering charge 5Q. Charge 5Q lies outside the surface, thus it makes no contribution to electric flux through the given surface.