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?

1.	resistance of \(19.92~ \mathrm{k} \Omega\) parallel to the galvanometer
2.	resistance of \(19.92~ \mathrm{k} \Omega\) in series with the galvanometer
3.	resistance of \(20 ~\Omega\) parallel to the galvanometer
4.	resistance of \(20~ \Omega\) in series with the galvanometer

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 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. \(5.37 \times10^{-3} ~\mathrm{T} \)

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 neutron, a proton, an electron and an \(\alpha\text-\)particle enter a region of the uniform magnetic field with the same velocity. The magnetic field is perpendicular and directed into the plane of the paper. The tracks of the particles are labelled in the figure. Which track will the \(\alpha\text-\)particle follow?
             

A charged particle is projected through a region in a gravity-free space. If it passes through the region with constant speed, then the region may have:
1. \(\vec{E}=0, \vec{B} \neq 0\)
2. \(\vec{E} \neq 0, \vec{B} \neq 0\)
3. \(\vec{E} \neq 0, \vec{B}=0\)
4. Both (1) & (2)

Which one of the following expressions represents Biot-Savart's law? Symbols have their usual meanings.

On connecting a shunt of \(10 ~ \Omega,\) the deflection in a moving coil galvanometer falls from 40 divisions to 6 divisions. What is the resistance of the galvanometer?

Magnetic field at the outer surface of long hollow cylindrical shells of radius R and carrying current I is B. What is the magnetic field at a distance of $\frac{3R}{2}$ from the axis of the cylindrical shell?