A flat circular coil has 200 identical loops of very thin wire. Each loop has an area of $0.12 \mathrm {~m} ^ { 2 }$ and carries $0.50 \mathrm {~A}$ of current. This coil is placed in a magnetic field of $0.050 \mathrm {~T}$ oriented at $30 ^ { \circ }$ to the plane of the loop. What is the magnitude of the magnetic torque on the coil?
A) $2.5 \mathrm {~N} \cdot \mathrm { m }$
B) $0.25 \mathrm {~N} \cdot \mathrm { m }$
C) $0.52 \mathrm {~N} \cdot \mathrm { m }$
D) $5.2 \mathrm {~N} \cdot \mathrm { m }$

Question

Quizplus · Accepted Answer

The magnetic torque on the coil is given by the formula $\tau = n \cdot I \cdot A \cdot B \cdot \sin(\theta)$, where $n$ is the number of loops, $I$ is the current, $A$ is the area of each loop, $B$ is the magnetic field, and $\theta$ is the angle between the magnetic field and the normal to the plane of the coil. Substituting the given values: $\tau = 200 \cdot 0.50 \cdot 0.12 \cdot 0.050 \cdot \sin(30^\circ) = 0.52 \mathrm {~N} \cdot \mathrm { m }$.

A Flat Circular Coil Has 200 Identical Loops of Very 0.12 m20.12 \mathrm {~m} ^ { 2 }0.12 m2

A Flat Circular Coil Has 200 Identical Loops of Very $0.12 \mathrm {~m} ^ { 2 }$