The angles of dip are $30^{\circ}$ and $45^{\circ}$ at two different places. The ratio of the horizontal components of the Earth's magnetic field at these places will be:

Consider the plane $S$ formed by the dipole axis and the axis of the Earth. Let $P$ be a point on the magnetic equator and in plane $S$. Let $Q$ be a point of intersection of the geographical and magnetic equators. Obtain the declination and dip angles at $P$ and $Q$.

At an angle of $30^{\circ}$ to the magnetic meridian,the apparent dip is $45^{\circ}$. Find the true dip.

The horizontal component of Earth's magnetic field at a place is $3.5 \times 10^{-5} \,T$. $A$ very long straight conductor carrying a current of $\sqrt{2} \,A$ in the direction from South-East to North-West is placed. The force per unit length experienced by the conductor is $..............$ $\times 10^{-6} \,N/m$.

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

$A$ 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