Answer to Question #196040 in Electric Circuits for Kenma

Question

(a) What is the maximum torque on a 150-turn square loop of wire 18.0 cm on a side that carries a 50.0-A current in a 1.60-T field? _____ N-m

(b) What is the torque when θ is 10.9°? _____ N-m

Round your answers to the nearest 1 decimal place

Answer 1

Explanations & Calculations

• The Torque generated by a loop of a conductor placed in a uniform magnetic field is given by

$\qquad\qquad \begin{aligned} \small \tau&=\small BiNA\sin\theta \end{aligned}$

• The angle is measured with respect to the plane of the magnetic field such that at 90 degrees the torque achieves its maximum as $\small \sin 90 = 1$.
• That is when the loop positions itself perpendicular to the field.
• Similarly, no torque is experienced when the loop is parallel to the field when $\small \theta = 0$ as $\small \sin 0 =0$.
• Then,

$\qquad\qquad \begin{aligned} \small \tau_{max}&=\small BiNA\\ &= \small 1.60T\times50A\times150\times(0.18m)^2\\ &=\small \bold{388.8\,Nm}\\\\ \tau_{@\,\theta=10.9^0}&=\small 1.60\times50\times150\times(1.8)^2\times\sin10.9\\ &=\small \bold{73.5\,Nm} \end{aligned}$