Two small bar magnets are placed in the air at a distance r apart. The magnetic force between them is proportional to:

1. $r^2$

2. $r^{-2}$

3. $r^{-3}$

4. $r^{-4}$

A magnet of magnetic moment 20 C.G.S. units are freely suspended in a uniform magnetic field of intensity 0.3 C.G.S. units. The amount of work done in deflecting it by an angle of ${30}^o$ in C.G.S. units is

1. 6

2. $3\sqrt{3}$

3. $3(2-\sqrt{3})$

4. 3

The magnetic field due to a short magnet at a point on its axis at a distance X cm from the middle point of the magnet is 200 Gauss. The magnetic field at a point on the neutral axis at a distance of X cm from the middle of the magnet is:

1. 100 Gauss

2. 400 Gauss

3. 50 Gauss

4. 200 Gauss

If a bar magnet of magnetic moment M is freely suspended in a uniform magnetic field of strength B, the work done in rotating the magnet through an angle is

1. $MB(1-\sin \theta )$

2. $MB\sin \theta$

3. $MB\cos \theta$

4. $MB(1-\cos \theta )$

A bar magnet of magnetic moment 10⁴J/T is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from a direction parallel to a horizontal magnetic field of 4×10^–5 T to a direction 60° from the field will be

1. 0.2 J                          2. 2.0 J

3. 4.18 J                        4. 2 × 10² J

A magnet of magnetic moment $50\widehat{i<mspace\; width="1em"></mspace>}A-m^2$ is placed along the x-axis in a magnetic field $\overrightarrow{B}=(0.5\hat{i}+3.0\hat{j})T$. The torque acting on the magnet is

1. 175 $\hat{k}$ N-m

2. 150 $\hat{k}$ N-m

3. 75 $\hat{k}$ N-m

4. 25$\sqrt{37}$ $\hat{k}$ N-m

Magnets \(A\) and \(B\) are geometrically similar but the magnetic moment of \(A\) is twice that of \(B\). If \(T_1\) and \(T_2\) be the time periods of the oscillation when their like poles and unlike poles are kept together respectively, then \(\frac{T_1}{T_2}\) will be:
1. \(\frac{1}{3}\)
2. \(\frac{1}{2}\)
3. \(\frac{1}{\sqrt{3}}\)
4. \(\sqrt{3}\)

A thin rectangular magnet suspended freely has a period of oscillation equal to \(T\). Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is \(T'\), then ratio \(\frac{T'}{T}\) is:
1. \(\frac{1}{4}\)
2. \(\frac{1}{2\sqrt{2}}\)
3. \(\frac{1}{2}\)
4. \(2\)

A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is \(2^{\frac{5}{4}}\) seconds. One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in seconds is:
1. \(2^\frac{1}{4}\)
2. \(2^\frac{1}{2}\)
3. \(2\)
4. \(2^\frac{3}{4}\)

Each atom of an iron bar\(\) (5 cm × 1 cm × 1 cm) has a magnetic moment \(1 . 8 \times 10^{- 23} A m^{2}\). Knowing that the density of iron is \(7 . 78 \times 10^{3} k g m^{- 3}\) atomic weight is 56 and Avogadro's  number is \(6 . 02 \times 10^{23}\) the magnetic moment of the bar in the state of magnetic saturation will be:

1. 4.75 Am²                 

2. 5.74 Am²

3. 7.54 Am²                 

4. 75.4 Am²