If the magnetic declination at a place is known to be $15^{\circ} \, E$,and a compass needle points as shown in the figure,then the geographic north is represented by which numbered direction?

The relation between $Z_E, H_E$,and $B_E$ is . . . . . . .

$A$ 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 magnetic field of the Earth at the equator is approximately $4 \times 10^{-5} \, T$. The radius of the Earth is $6.4 \times 10^6 \, m$. Then the dipole moment of the Earth will be nearly of the order of:

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

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.