What is the magnitude of the equatorial and a | vedclass

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Question

(A) Given: Magnetic moment $m = 0.40 \; A m^{2}$,distance $r = 50 \; cm = 0.5 \; m$. The length of the magnet $(5.0 \; cm)$ is small compared to the d

Vedclass · Accepted Answer

$B_{E} = 3.2 	imes 10^{-7} \; T, B_{A} = 6.4 	imes 10^{-7} \; T$

Vedclass · Answer

(A) Given: Magnetic moment $m = 0.40 \; A m^{2}$,distance $r = 50 \; cm = 0.5 \; m$. The length of the magnet $(5.0 \; cm)$ is small compared to the distance $(50 \; cm)$,so we use the short dipole approximation.For the equatorial field $(B_{E})$:$B_{E} = \frac{\mu_{0} m}{4 \pi r^{3}} = \frac{10^{-7} 	imes 0.40}{(0.5)^{3}} = \frac{10^{-7} 	imes 0.40}{0.125} = 3.2 	imes 10^{-7} \; T$.For the axial field $(B_{A})$:$B_{A} = \frac{\mu_{0} 2m}{4 \pi r^{3}} = 2 	imes B_{E} = 2 	imes 3.2 	imes 10^{-7} = 6.4 	imes 10^{-7} \; T$.

What is the magnitude of the equatorial and axial fields due to a bar magnet of length $5.0 \; cm$ at a distance of $50 \; cm$ from its mid-point? The magnetic moment of the bar magnet is $0.40 \; A m^{2}$.

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