The true value of angle of dip at a place is $60^o$, the apparent dip in a plane inclined at an angle of $30^o$ with magnetic meridian is

A current carrying coil is placed with its axis perpendicular to $ N-S $ direction. Let horizontal component of earth's magnetic field be $H_o$ and magnetic field inside the loop is $H$. If a magnet is suspended inside the loop, it makes angle $\theta $ with $H$. Then $\theta $$=$

Assume the dipole model for earth’s magnetic field $\mathrm{B}$ which is given by

${{\rm{B}}_{\rm{v}}} = $ vertical component of magnetic field

$ = \frac{{{\mu _0}}}{{4\pi }}\frac{{2m\,\cos \theta }}{{{r^3}}}$

${{\rm{B}}_H} = $ Horizontal component of magnetic field

${{\rm{B}}_H} = \frac{{{\mu _0}}}{{4\pi }}\frac{{m\,\sin \theta }}{{{r^3}}}$

$\theta $ $= 90^{°}$ -latitude as measured from magnetic equator.

$(a)$ Find loci of points for which : dip angle is zero;

Magnetic meridian is a

A telephone cable at a place has four long straight horizontal wires carrying a current of $1.0\; A$ in the same direction east to west. The earth's magnetic field at the place is $0.39 \;G ,$ and the angle of dip is $35^{\circ} .$ The magnetic declination is nearly zero. What are the resultant magnetic fields at points $4.0\; cm$ below and above the cable?

A dip circle is adjusted so that its needle moves freely in the magnetic meridian. In this position, the angle of dip is $40°$. Now the dip circle is rotated so that the plane in which the needle moves makes an angle of $30°$ with the magnetic meridian. In this position the needle will dip by an angle