Isogonic lines on a magnetic map will have

$A$ compass needle oscillates $20$ times per minute at a place where the dip is $30^{\circ}$ and $30$ times per minute where the dip is $60^{\circ}$. The ratio of total magnetic field due to the earth at the two places respectively is $\frac{4}{\sqrt{x}}$. The value of $x$ is $............$.

The angle of dip at a place is $30^{\circ}$,and the horizontal component of the Earth's magnetic field is $5 \times 10^{-5} \, T$. Calculate the vertical component and the total magnetic field at that place.

What is the angle between the axis of rotation and the magnetic axis of the Earth (in $°$)?

At a certain place,the horizontal component of earth's magnetic field is $\sqrt{3}$ times the vertical component. The angle of dip at that place is....$^o$

Let $m$ and $r$ be the dipole moment and radius of the Earth,respectively. Then,the Earth's magnetic field at the equator is