A bar magnet of length l and magnetic dipole moment M is bent to form an arc which subtends an angle of $120°$ at centre. The new magnetic dipole moment will be

1.  $\frac{3\mathrm{M}}{2\mathrm{\pi }}$

2.  $\frac{3\sqrt{3}\mathrm{M}}{2\mathrm{\pi }}$

3.  $\frac{3\mathrm{M}}{\mathrm{\pi }}$

4.  $\frac{2\mathrm{M}}{\mathrm{\pi }}$

$$\begin{gathered} \mathrm{A} \mathrm{small} \mathrm{bar} \mathrm{magnet} \mathrm{is} \mathrm{placed} \mathrm{with} \mathrm{its} \mathrm{north} \mathrm{pole} \mathrm{facing} \mathrm{magnetic} \mathrm{north} \\ \mathrm{pole}. \mathrm{The} \mathrm{neutral} \mathrm{points} \mathrm{are} \mathrm{located} \mathrm{at} \mathrm{distance} \mathrm{r} \mathrm{from} \mathrm{its} \mathrm{centre}. \mathrm{If} \\ \mathrm{magnet} \mathrm{is} \mathrm{rotated} \mathrm{by} {180}^0, \mathrm{neutral} \mathrm{point} \mathrm{shall} \mathrm{be} \mathrm{obtained} \mathrm{at} \\ \mathrm{distance}: \\ 1. 2\mathrm{r} 2. \sqrt{2}\mathrm{r} \\ 3. 2^{-\frac{1}{3}}\mathrm{r} 4. \frac{\mathrm{r}}{2\sqrt{2}} \end{gathered}$$

The unit of pole strength is

(1) $A{m}^2$

(2) Am

(3) $\frac{A^2}{m}$

(4) $\frac{A^2}{m^2}$

$$\begin{gathered} \mathrm{If} \mathrm{a} \mathrm{magnet} \mathrm{is} \mathrm{suspended} \mathrm{at} \mathrm{angle} 30° \mathrm{to} \mathrm{the} \mathrm{magnetic} \mathrm{meridian}, \mathrm{the} \mathrm{dip} \mathrm{needle} \mathrm{makes} \mathrm{an} \mathrm{angle} \mathrm{of} 45° \mathrm{with} \mathrm{the} \mathrm{horizontal}. \\ \mathrm{The} \mathrm{value} \mathrm{of} \mathrm{re}al \mathrm{dip} \mathrm{angle} \mathrm{at} \mathrm{the} \mathrm{place} \mathrm{is} \end{gathered}$$

1.  ${\tan }^{-1} \frac{\sqrt{3}}{2}$

2.  ${\tan }^{-1} 1$

3.  ${\tan }^{-1 }\frac{1}{2}$

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

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

(1) $r^2$

(2) $r^{-2}$

(3) $r^{-3}$

(4) $r^{-4}$

The vertical component of the earths magnetic field is zero at

(1) Magnetic poles

(2) Magnetic equator

(3) Geographic poles

(4) Geographic equator

A short magnetic dipole is placed at the origin with its dipole movement directed along the +x-axis. If magnetic field induction at a point P (r, 0) is B$\hat{i}$, the magnetic field induction at point Q(0,2r) will be

(1) $-\frac{B}{16}\hat{i}$

(2) $-\frac{B}{8}\hat{j}$

(3) $\frac{B}{16}\hat{j}$

(4) $-\frac{B}{16}\hat{j}$

The magnetic field at a point x on the axis of a small bar magnet is equal to the field at a point y on the equator of the same magnet. The ratio of the distances of x and y from the centre of the magnet is
(a) $2^{-3}$

(b) $2^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

(c) $2^3$

(d) $2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

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
(a) 6

(b) $3\sqrt{3}$

(c) $3(2-\sqrt{3})$

(d) 3

The magnetic field due to a short magnet at a point on its axis at 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 X cm from the middle of the magnet is

1. 100 Gauss               2. 400 Gauss
3. 50 Gauss                 4. 200 Gauss