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.

At the magnetic poles of the earth,a compass needle will be

Assertion : The true geographic north direction is found by using a compass needle.
Reason : The magnetic meridian of the earth is along the axis of rotation of the earth.

The Earth's magnetic field was flipped by $180^{\circ}$ a million years ago. This flip was relatively rapid and took $10^5 \, \text{years}$. Then, the average change in orientation per year during the flip was closest to ............ $s$.

What are the Earth's magnetic elements? Define them and list them.

Assume the dipole model for Earth's magnetic field $B$,which is given by:
$B_{V} = \text{vertical component of magnetic field} = \frac{\mu_{0}}{4\pi} \frac{2m \cos \theta}{r^{3}}$
$B_{H} = \text{horizontal component of magnetic field} = \frac{\mu_{0}}{4\pi} \frac{m \sin \theta}{r^{3}}$
where $\theta = 90^{\circ} - \text{latitude}$ as measured from the magnetic equator.
$(a)$ Find the loci of points for which $|\vec{B}|$ is minimum.