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.
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 the axis.
Magnitude: ⁻⁴ T (or 0.96 G). Direction: Along the axis of the magnet, in the direction of the magnetic moment (from south to north pole).
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 the equatorial lines (normal bisector) of the magnet.
Magnitude: ⁻⁴ T (or 0.48 G). Direction: Opposite to the magnetic moment direction (from north to south pole of the magnet).
Explanation
This problem applies the standard formulas for magnetic field due to a bar magnet at points on its axis and equatorial line. The context provides these formulas: for axial field B = (μ₀/4π)(2m/r³) and for equatorial field B = (μ₀/4π)(m/r³). The negative sign in the equatorial formula indicates the field direction is opposite to the magnetic moment. These formulas are valid when distance r is much greater than the magnet size l.