$A$ magnetic compass needle oscillates $30$ times per minute at a place where the angle of dip is $45^{\circ}$,and $40$ times per minute where the angle of dip is $30^{\circ}$. If $B_1$ and $B_2$ are respectively the total magnetic field due to the earth at the two places,then the ratio $B_1/B_2$ is best given by:

The lines joining the places of the same horizontal intensity are known as

At a certain location in Africa,a compass points $12^{\circ}$ West of the geographic North. The North tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points $60^{\circ}$ above the horizontal. The horizontal component of the earth's field is measured to be $0.16\, G$. The magnitude of the earth's field at the location will be

The angle between the Earth's magnetic axis and the Earth's geographical axis is approximately $... ^\circ$.

If $\theta_1$ and $\theta_2$ are 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:

$A$ dip needle lies initially in the magnetic meridian when it shows an angle of dip $\theta$ at a place. The dip circle is rotated through an angle $x$ in the horizontal plane and then it shows an angle of dip $\theta'$. Then $\frac{\tan \theta'}{\tan \theta}$ is