Two identical dipoles each of magnetic moment | vedclass

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Question

(A) Given: Magnetic moment $M = 1.0 \, A-m^2$,distance between dipoles $d = 2 \, m$. The point is midway,so the distance from each dipole to the point

Vedclass · Accepted Answer

$\sqrt{5} 	imes 10^{-7} \, T$

Vedclass · Answer

(A) Given: Magnetic moment $M = 1.0 \, A-m^2$,distance between dipoles $d = 2 \, m$. The point is midway,so the distance from each dipole to the point is $r = 1 \, m$.For the first dipole,the point lies on its axial line. The magnetic field is $B_1 = \frac{\mu_0}{4\pi} \frac{2M}{r^3} = 10^{-7} 	imes \frac{2 	imes 1}{1^3} = 2 	imes 10^{-7} \, T$.For the second dipole,the point lies on its equatorial line. The magnetic field is $B_2 = \frac{\mu_0}{4\pi} \frac{M}{r^3} = 10^{-7} 	imes \frac{1}{1^3} = 1 	imes 10^{-7} \, T$.Since the axes are perpendicular,the fields $B_1$ and $B_2$ are perpendicular to each other.The resultant magnetic field is $B_{net} = \sqrt{B_1^2 + B_2^2} = \sqrt{(2 	imes 10^{-7})^2 + (1 	imes 10^{-7})^2} = \sqrt{4 + 1} 	imes 10^{-7} = \sqrt{5} 	imes 10^{-7} \, T$.

Two identical dipoles each of magnetic moment $1.0 \, A-m^2$ are placed at a separation of $2 \, m$ with their axes perpendicular to each other. What is the magnetic field at a point midway between the dipoles?

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