A square loop with a side l is held in a uniform magnetic field B, such that its plane making an angle \(\alpha\)with B. A current I flows through the loop. What will be the torque experienced by the loop in this position?

1. ${\mathrm{Bil}}^2$

2. ${\mathrm{Bil}}^2\mathrm{sin\alpha }$

3. ${\mathrm{Bil}}^2\mathrm{cos\alpha }$

4. Zero

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60°, and one of the fields has a magnitude of 1.2×10^-2 T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field?
 \(\left[\text{Given} :   \sin   15^ \circ = 0 . 26\right]\)
1. \( 7.29 \times10^{-3} ~\mathrm{T} \)
2. \( 4.39 \times10^{-3} ~\mathrm{T} \)
3. \( 6.18 \times10^{-3} ~\mathrm{T} \)
4. \(5.37 \times10^{-3} ~\mathrm{T} \)

Two identical current-carrying coaxial loops, carry current I in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C,

Which of the above statements are correct?
1. a and b
2. a and c
3. b and c
4. c and d

A wire of length \(L\) meters carrying a current of \(I\) amp is bent in the form of a circle. What is its magnetic moment?
1. \( \frac{{IL}^2}{4} ~\text{A}\text-\text{m}^2 \)
2. \( \frac{{I} \times \pi {L}^2}{4} ~\text{A}\text-\text{m}^2 \)
3. \( \frac{2 {IL}^2}{\pi}~\text{A}\text-\text{m}^2 \)
4. \( \frac{{IL}^2}{4 \pi}~\text{A}\text-\text{m}^2 \)

The galvanometer of resistance 80 Ω deflects a full scale for a potential of 20 mV. How much resistance is required for a voltmeter to deflect a full scale of 5 V to be made using this galvanometer?

A galvanometer of resistance, \(\mathrm G,\) is shunted by the resistance of \(\mathrm S\) ohm. How much resistance is to be put in series with the galvanometer to keep the main current in the circuit unchanged?

A closely wound solenoid of 2000 turns and an area of cross-section of 1.5 × 10^–4 m² carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field of 5 × 10^–2 Tesla, making an angle of 30^o with the axis of the solenoid. What will be the torque on the solenoid?

1. 1.5 × 10^–3 Nm

2. 1.5 × 10^–2 Nm

3. 3 × 10^–2 Nm

4. 3 × 10^–3 Nm

The resistances of three parts of a circular loop are as shown in the figure. What will be the magnetic field at the centre of O 
(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.  $\frac{2{\mathrm{\mu }}_0\mathrm{I}}{3\mathrm{a}}$

4.  0

Consider six wires with the same current flowing through them as they enter or exit the page. Rank the magnetic field's line integral counterclockwise around each loop, going from most positive to most negative.

1. B > C > D > A

2. B > C = D > A

3. B > A > C = D

4. C > B = D > A

A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that $\overrightarrow{\mathrm{B}}$ is in the plane of the coil. If due to a current i in the triangle, a torque τ acts on it, the side l of the triangle will be:

1. $\frac{2}{\sqrt{3}}\left(\frac{\tau }{\mathrm{Bi}}\right)$ $$

2. $\frac{1}{\sqrt{3}}\frac{\tau }{\mathrm{Bi}}$

3. $2{\left(\frac{\tau }{\sqrt{3}\mathrm{Bi}}\right)}^{\frac{1}{2}}$

4. $\frac{2}{\sqrt{3}}{\left(\frac{\tau }{\mathrm{Bi}}\right)}^{\frac{1}{2}}$