If a magnet is suspended at an angle 30^o to the magnetic meridian, it makes an angle of 45^o with the horizontal. The real dip is

(a)${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

(b)${\tan }^{-1}\left(\sqrt{3}\right)$

(c)${\tan }^{-1}\left(\sqrt{\frac{3}{2}}\right)$

(d)${\tan }^{-1}\left(\frac{2}{\sqrt{3}}\right)$

The true value of angle of dip at a place is 60^o, the apparent dip in a plane inclined at an angle of 30^o with magnetic meridian is

(1)${\tan }^{-1}\left(\frac{1}{2}\right)$

(2)${\tan }^{-1}\left(2\right)$

(3)${\tan }^{-1}\left(\frac{2}{3}\right)$

(4)None of these

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. \(2^\frac{3}{4}\)

A cylindrical rod magnet has a length of 5 cm and a diameter of 1 cm. It has a uniform magnetization of 5.30 × 10³Amp/m³. What is its magnetic dipole moment?

1. $1\times {10}^{-2} J/T$                   

2. $2.08\times {10}^{-2} J/T$

3. $3.08\times {10}^{-2} J/T$              

4. $1.52\times {10}^{-2} J/T$

Two magnets of equal mass are joined at right angles to each other as shown the magnet 1 has a magnetic moment 3 times that of magnet 2. This arrangement is pivoted so that it is free to rotate in the horizontal plane. In equilibrium what angle will the magnet 1 subtend with the magnetic meridian

1. ${\tan }^{-1}\left(\frac{1}{2}\right)$

2. ${\tan }^{-1}\left(\frac{1}{3}\right)$

3. ${\tan }^{-1}\left(1\right)$

4. $0°$

Two magnets \(A\) and \(B\) are identical and these are arranged as shown in the figure. Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point \(P\) which gets deflected through an angle \(\theta\) under the influence of magnets. The ratio of distance \(d_1\) and \(d_2\) will be:
   
1. \((2\tan\theta)^{\frac{1}{3}}\)
2. \((2\tan\theta)^{\frac{-1}{3}}\)
3. \((2\cot\theta)^{\frac{1}{3}}\)
4. \((2\cot\theta)^{\frac{-1}{3}}\)

Two short magnets of equal dipole moments M are fastened perpendicularly at their centres (figure). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is :

1. $\frac{{\mu }_0}{4\mathrm{\pi }} \frac{M}{d^3}$

2. $\frac{{\mu }_0}{4\mathrm{\pi }} \frac{M\sqrt{2}}{d^3}$

3. $\frac{{\mu }_0}{4\mathrm{\pi }} \frac{2\sqrt{2}M}{d^3}$

4. $\frac{{\mu }_0}{4\mathrm{\pi }} \frac{2M}{d^3}$

Two identical bar magnets with a length of 10 cm and weight 50 gm-weight are arranged

freely with their like poles facing in an inverted vertical glass tube. The upper magnet

hangs in the air above the lower one so that the distance between the nearest pole of the

magnet is 3mm. Pole strength of the poles of each magnet will be:

1. 6.64 amp$\times$m

2. 2 amp$\times$m

3. 10.25 amp$\times$m

4. None of these

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 $7.78\times {10}^3 kg{m}^{-3}$ 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

A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be 2 seconds. The same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be 2 seconds. Then the angle of dip is

1. 0^o                             2. 30^o

3. 45^o                           4. 90^o