Question

The magnetic field strength at a point at a distance 'd' from the centre on the axial line of a very short bar magnet of magnetic moment m, is



b. The magnetic induction at a distance '2d' from centre, on the equatorial line of a magnet of magnetic moment 8 m, will be

Answer 1

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The shortest distance between the two poles of a bar magnet is the magnetic length of the bar magnet (2l). The axial line of a bar magnet is a straight line passing through its centre and its poles. The equatorial line of a bar magnet is a straight line perpendicular to its axial line and passing through its centre. The magnetic moment M of a magnet is defined as the product of its magnetic length 2l and its pole strength m. Therefore, M = 2lm. The SI unit of magnetic moment M is ampere metre-square (Am2) or weber metre (Wb.m). The magnetic moment of a bar magnet is a vector quantity whose direction is along its axial line, from its south pole towards its north pole.

he length of barmagnet be 2l as shown in figure.  Let P be a point on the axis line at a distance d.

Magnetic induction at point P due to the poles of given barmagnet is given by




where m is the pole strength of the given bar magnet. Let us assume d >> l and consider the magnetic moment = m×2l = M, then we can write the above relation as

.........................................(1)

Let Q be a point on the equatorial line at a distance d from bar-magnet as shown in figure. Magnetic induction at a point Q is given by

 



Refer the diagram for the desciption of the induction vectors due to the poles and how the reultant vector is worked out.


Again by considering magnetic moment M = m×2l and d >> l, we can wite the above expression as