A rectangular coil (0.20 m × 0.80 m) has 200 turns and is in a uniform magnetic field of 0.30 T. When the orientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is 0.080 N ⋅ m. What is the current in the coil?
A) 5.0 mA
B) 1.7 A
C) 8.3 mA
D) 1.0 A
E) 42 mA

Question

Quizplus · Accepted Answer

The maximum torque ($\tau_{max}$) experienced by a coil in a magnetic field is given by the formula $\tau_{max} = NIBA\sin(\theta)$, where $N$ is the number of turns, $I$ is the current, $B$ is the magnetic field strength, $A$ is the area of the coil, and $\theta$ is the angle between the normal to the plane of the coil and the magnetic field direction. At maximum torque, $\sin(\theta) = 1$. Given $\tau_{max} = 0.080 N \cdot m$, $N = 200$, $B = 0.30 T$, and $A = 0.20 m \times 0.80 m = 0.16 m^2$, we can solve for $I$:$$0.080 = 200 \cdot I \cdot 0.30 \cdot 0.16$$$$I = \frac{0.080}{200 \cdot 0.30 \cdot 0.16}$$$$I = \frac{0.080}{9.6}$$$$I = 0.00833 A$$$$I = 8.3 mA$$

A Rectangular Coil (0