Which of the following relations is correct in the context of Earth's magnetism?

Choose the correct option regarding the relationship between true dip $(\phi)$ and apparent dip $(\phi^{\prime})$:

At a certain place,the angle of dip is $30^{\circ}$ and the horizontal component of the Earth's magnetic field is $0.5 \ G$. The Earth's total magnetic field (in $G$) at that place is:

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

$A$ 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

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