Torque on a square loop

Problem

A square loop of side $\ell = 10$ cm carries a current $i = 2$ A and is immersed in a uniform field $B = 0{,}25$ T. The magnetic moment $\vec\mu$ makes an angle of $60^\circ$ with $\vec B$. Calculate the magnitude of the torque applied to the loop.

Solution

The area of the loop is $A = \ell^2 = (0{,}10)^2 = 0{,}01\;\text{m}^2$. The magnetic moment is $\mu = iA$ and the torque is $\vec M = \vec\mu\times\vec B$, with magnitude $M = iAB\sin\beta = 2\cdot 0{,}01\cdot 0{,}25\cdot\sin 60^\circ = 0{,}005\cdot 0{,}866$ $\ev{M \approx 4{,}3\cdot 10^{-3}\;\text{N}\cdot\text{m}}$ The result is of the order of $5\cdot 10^{-3}\;\text{N}\cdot\text{m}$.

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Topics: Magnetism Concepts: Magnetic dipole · Torque