Question

A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earth’s magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null-point (i.e., 14 cm) from the centre of the magnet? (At null points, the field due to a magnet is equal and opposite to the horizontal component of earth’s magnetic field.)

Answer 1

Hint: The given problem is from earth magnetism and based on the concept that at equatorial lines the magnetic field intensity is half of the magnetic field intensity at the axis. So we use this property of magnet to solve the given problem.

Complete step by step answer:
According to earth magnetism at null point (and along the axis), earth’s magnetic field and bar’s magnetic field are opposite in direction. And on the equatorial line, the bar's magnetic field is opposite in direction to its field on the axis. Hence, on the equatorial line, the two fields add up.

As per the given condition in question, the null point is on the axis of the bar magnet. Therefore
${B_1} = \dfrac{{{\mu _0}}}{{4\pi }}\dfrac{{2M}}{{{d^3}}} = H = 0.36G$
Where ${\mu _0}$= Magnetic permeability of vacuum
M= Magnetic dipole moment
d= Distance from centre of bar magnet
As we know that on the equatorial line of magnet at the same distance (d), field intensity due to the magnet is half of the field intensity at the axis. So at equatorial the field intensity is given by
${B_2} = \dfrac{{{\mu _0}}}{{4\pi }}\dfrac{M}{{{d^3}}} = \dfrac{H}{2}$

The direction of this magnetic field is opposite to ${B_1}$. So at this point two fields add up.
Therefore the resultant field intensity at equatorial point is given by
$
  B = {B_2} + H \\
  B = \dfrac{H}{2} + H \\
  B = \dfrac{{3H}}{2} \\
  B = \dfrac{3}{2} \times 0.36G \\
  B = 0.54G \\
$
So, the total magnetic field at equatorial point is B=0.54 Gauss. The direction of the magnetic field is in the direction of the earth's magnetic field.

Note: Sometimes we ignore the direction of the magnetic field at equatorial point and solve the problem. That’s why we get wrong results. We should always remember that the direction of magnetic field intensity at equatorial point is opposite to axial point.