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 \(\frac{q}{\epsilon_0}\) where \(q\) is the charge enclosed by the surface. Thus, from the figure,

The total charge inside the surface is \(= Q - 2Q = -Q\)
The total flux through the surface of the sphere \(=-\frac{Q}{\epsilon_0}\)

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

Now, consider the charge \(5Q.\)
The charge \(5Q\) 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 \(5Q\) is zero.
Hence, option (2) is the correct answer.

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