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

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

1.  ${\tan }^{-1} \frac{\sqrt{3}}{2}$

2.  ${\tan }^{-1} 1$

3.  ${\tan }^{-1 }\frac{1}{2}$

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

The vertical component of the earths magnetic field is zero at

(1) Magnetic poles

(2) Magnetic equator

(3) Geographic poles

(4) Geographic equator

A neutral point is obtained at the centre of a vertical circular coil carrying current. The angle between the plane of the coil and the magnetic meridian is :

a) 0                           (b) 45°

(c) 60°                       (d) 90°

A bar magnet of length 3 cm has points A and B along its axis at distances of 24 cm and 48 cm on the opposite sides. Ratio of magnetic fields at these points will be

(a) 8                               (b)$\frac{1}{2\sqrt{2}}$

(c) 3                               (d) 4

A dip needle in a plane perpendicular to magnetic meridian will remain

(a) Vertical

(b) Horizontal

(c) In any direction

(d) At an angle of dip to the horizontal

If the angles of dip at two places are 30^o and 45^o respectively, then the ratio of horizontal  components of earth's magnetic field at the two places will be

(a) $\sqrt{3}:\sqrt{2}$                       (b) $1:\sqrt{2}$

(c) $1:\sqrt{3}$                          (d) 1:2

A line passing through places having zero value of magnetic dip is called

(a) Isoclinic line             (b) Agonic line

(c) Isogonic line             (d) Aclinic line

The earth's magnetic field at a certain place has a horizontal component 0.3 Gauss and the total strength 0.5 Gauss. The angle of dip is

(a) ${\tan }^{-1}\left(\frac{3}{4}\right)$                      (b) ${\sin }^{-1}\left(\frac{3}{4}\right)$

(c) ${\tan }^{-1}\left(\frac{4}{3}\right)$                      (d) ${\sin }^{-1}\left(\frac{3}{5}\right)$

At a certain place, the horizontal component B₀ and the vertical component V₀ of the earth's magnetic field are equal in magnitude. The total intensity at the place will be

1. $B_0$                            2. $B_0^2$

3. $2B_0$                          4. $\sqrt{2}{B}_0$