Three wires of equal lengths are bent in
the form of loops. One of the loops is
a circle, another is a semi-circle and the
third one is a square. They are placed
in a uniform magnetic field parallel to the 

plane of loop  and the same

electric current is passed through
them. Which of the following loop
configurations will experience greater
torque ?

1. Circle
2. Semi-circle
3. Square
4. All of them

Two identical coils, each with N turns
and radius R are placed coaxially at a
distance R as shown in the figure. If
I is the current passing through the
loops in the same direction, then the
magnetic field at a point P at a distance
of R/2 from the centre of each coil is

$1. \frac{8\mathrm{N}{\mu }_{\mathrm{o}}\mathrm{I}}{\sqrt{5}\mathrm{R}}$
$2. \frac{8\mathrm{N}{\mu }_{\mathrm{o}}\mathrm{I}}{5^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\mathrm{R}}$
$3. \frac{8\mathrm{N}{\mu }_{\mathrm{o}}\mathrm{I}}{5\mathrm{R}}$
$4. \frac{4\mathrm{N}{\mu }_{\mathrm{o}}\mathrm{I}}{\sqrt{5}\mathrm{R}}$

A wire of length l carrying a current I along the Y direction is
kept in a magnetic field given by $\overrightarrow{\mathrm{B}} = \frac{\beta }{\sqrt{3}}\left(\hat{i} +\hspace{0.17em}\hat{\mathrm{j}} +\hspace{0.17em}\hat{\mathrm{k}}\right)T.$ The
magnitude of Lorentz force acting on the wire is:

$1. \sqrt{\frac{2}{3}}\mathrm{\beta Il}$
$2. \sqrt{\frac{1}{3}}\mathrm{\beta Il}$
$3. \sqrt{2}\mathrm{\beta Il}$
$4. \sqrt{\frac{1}{2}}\mathrm{\beta Il}$

A non-conducting charged ring
carrying a charge of q, mass m and
radius r is rotated about its axis with
constant angular speed ω. Find the
ratio of its magnetic moment with
angular momentum is

$1. \frac{\mathrm{q}}{\mathrm{m}}$
$2. \frac{2\mathrm{q}}{\mathrm{m}}$
$3. \frac{\mathrm{q}}{2\mathrm{m}}$
$4. \frac{\mathrm{q}}{4\mathrm{m}}$

In a square loop made with a wire of uniform cross-section current I enters from point A and leaves from point B. The magnetic field strength at the centre of the square is :-

1. zero

2. $\frac{{\mathrm{\mu }}_{0}12\sqrt{2}}{4\mathrm{\pi a}}$

3. $\frac{4\sqrt{2}{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi a}}$

4. $\frac{2\sqrt{2}{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{a}}$

The magnetic field at center O of the arc shown in the figure is:

1. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}}[\sqrt{2}+\mathrm{\pi }]$

2. $\frac{\mathrm{\mu I}}{2\mathrm{\pi r}}[\frac{\mathrm{\pi }}{4}+(\sqrt{2}-1\left)\right]$

3. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}}[\sqrt{2}-\mathrm{\pi }]$

4. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}}[2+\frac{\mathrm{\pi }}{4}]$

The resistances of three parts of a circular loop are as shown in the figure. The magnetic field at the centre O is (current enters at A and leaves at B and C as shown):

1. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{6\mathrm{a}}$

2. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{3\mathrm{a}}$

3. $\frac{2}{3}\frac{{\mathrm{\mu }}_0\mathrm{I}}{\mathrm{a}}$

4. zero

The magnetic induction along the axis of an air solenoid is 0.03 Tesla. On placing an iron core inside the solenoid the magnetic induction becomes 15 Tesla. The relative permeability of the iron core will be:

1. 300

2. 500

3. 700

4. 900

A circular coil of radius 5 cm and 50
turns carries a current of 3 amperes. The
magnetic dipole moment of the coil is
nearly:
1. 1.0 A m${}^2$
2. 1.2 A m${}^2$
3. 0.5 A m${}^2$
4. 0.8 A m${}^2$

A particle having mass m and charge
q is accelerated through a potential
difference V. Find the force experienced
when it is kept under perpendicular
magnetic field $\overrightarrow{\mathrm{B}}$.

$1. \sqrt{\frac{2{\mathrm{q}}^3\mathrm{BV}}{\mathrm{m}}}$
$2. \sqrt{\frac{{\mathrm{q}}^3{\mathrm{B}}^2\mathrm{V}}{2\mathrm{m}}}$
$3. \sqrt{\frac{2{\mathrm{q}}^3{\mathrm{B}}^2\mathrm{V}}{\mathrm{m}}}$
$4. \sqrt{\frac{2{\mathrm{q}}^3\mathrm{BV}}{{\mathrm{m}}^3}}$