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10
MCQ (Multiple Correct Answer)

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

A
$\oint_s \mathbf{E} . \mathrm{dS} \neq 0$ on any surface
B
$\oint_s \mathbf{E} \cdot \mathbf{d S}=0$ if the charge is outside the surface
C
$\oint_s \mathbf{E} \mathbf{d S}$ could not be defined
D
$\boldsymbol{\oint}_s \mathbf{E} \mathbf{d S}=\frac{q}{\varepsilon_0}$ if charges of magnitude $q$ were inside the surface
11
MCQ (Multiple Correct Answer)

Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region,

A
the electric field is necessarily zero
B
the electric field is due to the dipole moment of the charge distribution only
C
the dominant electric field is $\propto \frac{1}{r_3}$, for large $r$, where $r$ is the distance from a origin in this regions
D
the work done to move a charged particle along a closed path, away from the region, will be zero
12
MCQ (Multiple Correct Answer)

Refer to the arrangement of charges in figure and a Gaussian surface of 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 sphere due to $5 Q$ is zero
D
field on the surface of sphere due to $-2 Q$ is same everywhere
13
MCQ (Multiple Correct Answer)

A positive charge $Q$ is uniformly distributed along a circular ring of radius R.A small test charge $q$ is placed at the centre of the ring figure. Then,

A
if $q>0$ and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre
B
if $q<0$ and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring
C
if $q<0$, it will perform SHM for small displacement along the axis
D
$q$ at the centre of the ring is in an unstable equilibrium within the plane of the ring for $q>0$
14
Subjective

An arbitrary surface encloses a dipole. What is the electric flux through this surface?

Explanation

From Gauss' law, the electric flux through an enclosed surface is given by $\oint_s E . d S=\frac{q}{\varepsilon_0}$.

Here, $q$ is the net charge inside that enclosed surface.

Now, the net charge on a dipole is given by $-q+q=0$

$\therefore \quad$ Electric flux through a surface enclosing a dipole $=\frac{-q+q}{\varepsilon_0}=\frac{0}{\varepsilon_0}=0$

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