In: Physics
Assume that the loop is initially positioned at θ=30∘ and the current flowing into the loop is 0.500 A . If the magnitude of the magnetic field is 0.300 T , what is τ, the net torque about the vertical axis of the current loop due to the interaction of the current with the magnetic field?
the net torque about the vertical axis of the current loop is,
$$ \tau=N I B A \sin \phi $$
Here, \(\phi\) is the angle between the normal (to the loop) and
the magnetic field.
$$ \phi=90^{\circ}-30^{\circ}=60^{\circ} $$
Hence, the net torque about the vertical axis of the current loop is,
$$ \begin{aligned} \tau &=(1) I B A \sin 60^{\circ} \\ &=I B A \sin 60^{\circ} \end{aligned} $$
If \(I=0.500 \mathrm{~A}, B=0.300 \mathrm{~T}, A=(0.04 \mathrm{~m})(0.02 \mathrm{~m})\), then the net
torque about the vertical axis of the current loop is,
$$ \begin{array}{l} \tau=(0.500 \mathrm{~A})(0.300 \mathrm{~T})(0.04 \mathrm{~m})(0.02 \mathrm{~m}) \sin 60^{\circ} \\ \tau \approx 0.000104 \mathrm{~N} \cdot \mathrm{m} \end{array} $$