A short bar magnet has a magnetic moment of 0.48 J T–1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis,
(b) the equatorial lines (normal bisector) of the magnet.
A short bar magnet has a magnetic moment of 0.48 J T–1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis,
(b) the equatorial lines (normal bisector) of the magnet.

Magnetic moment of the bar magnet is given by M = 0.48 J T–1

  • Distance, d = 10 cm = 0.1 m

The magnetic field at distance d from the magnet’s centre on the axis can be calculated using the following formula –

$B=\frac{{{\mu }_{0}}2M}{4\pi {{d}^{3}}}$

Where \[{{\mu }_{0}}=4\pi \times {{10}^{-7}}Tm{{A}^{-1}}\]

$B=\frac{4\pi \times {{10}^{-7}}\times 2\times 0.48}{4\pi \times {{(0.1)}^{3}}}$

$B=0.96G$

The magnetic field is along the S-N direction.

(b)                                                                         

The magnetic field at a distance 10 cm (i.e., d = 0.1 m) on the equatorial line of the magnet is given by the following relation –

$B=\frac{{{\mu }_{0}}M}{4\pi {{d}^{3}}}$

Where \[{{\mu }_{0}}=4\pi \times {{10}^{-7}}Tm{{A}^{-1}}\]

$B=\frac{4\pi \times {{10}^{-7}}\times 0.48}{4\pi \times {{(0.1)}^{3}}}$

$B=0.48G$

The magnetic field is along the N – S direction.