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

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 \(𝜃\) under the influence of magnets. The ratio of distance \(d_1\) and \(d_2\) will be:

1. \((2   \tan   \theta) ^{1 / 3}\)

2. \((2   \tan   \theta) ^{(-1 / 3)}\)

3. \((2   \cot   \theta) ^{1 / 3}\)

4. \((2   \cot   \theta) ^{(-1 / 3)}\)

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:

The variation of magnetic susceptibility $\left(\chi \right)$ with temperature for a diamagnetic substance is best represented by:

1.		2.
3.		4.

The variation of magnetic susceptibility $\left(\chi \right)$ with absolute temperature T for a ferromagnetic material is

The relative permeability $\left({\mu }_r\right)$ of a ferromagnetic substance varies with temperature (T) according to the curve

(1) A                              

(2) B

(3) C                              

(4) D

The variation of the intensity of magnetisation \((I)\) with respect to the magnetising field \((H)\) in a diamagnetic substance is described by the graph:

If ${\theta }_1 and {\theta }_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given by 

(a) $co{t}^2\theta =co{t}^2{\theta }_1+co{t}^2{\theta }_2$

(b) ${\tan }^2\theta ={\tan }^2{\theta }_1-{\tan }^2{\theta }_2$

(c) $co{t}^2\theta =co{t}^2{\theta }_1-{\tan }^2{\theta }_2$

(d) ${\tan }^2\theta ={\tan }^2{\theta }_1-{\tan }^2{\theta }_2$

The magnetic susceptibility is negative for

1. paramagnetic material only

2. ferromagnetic material only

3. paramagnetic and ferromagnetic materials

4. diamagnetic material only