$A$ small bar magnet $A$ oscillates in a horizontal plane with a period $T$ at a place where the angle of dip is $60^o$. When the same needle is made to oscillate in a vertical plane coinciding with the magnetic meridian,its period will be

The vertical component of the earth's magnetic field is zero at a place where the angle of dip is.....$^o$

$A$ long vertical wire carries a steady current of $5.0 \, A$. $A$ sensitive magnetic compass is placed in a plane perpendicular to the wire and $10.0 \, cm$ south of it. It registers a deflection of $60^{\circ}$ north of east. The magnitude of the horizontal component of the earth's magnetic field is (permeability of free space is $4 \pi \times 10^{-7} \, N/A^2$):

The angle of dip at a place on the earth gives:

The angle of dip at a certain place is $30^o$. If the horizontal component of the earth's magnetic field is $H$,the intensity of the total magnetic field 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 $............$.