A flat circular wire loop of area $0.25 \mathrm {~m} ^ { 2 }$ carries a current of $5.0 \mathrm {~A}$. This coil lies on a horizontal table with the current flowing in the counterclockwise direction when viewed from above. At this point, the earth's magnetic field is $1.2 \times 10 ^ { - 5 } \mathrm {~T}$ directed $60 ^ { \circ }$ below the horizontal. What is the magnitude of the torque that the earth's magnetic field exerts on this loop?
A) $1.0 \times 10 ^ { - 5 } \mathrm {~N} \cdot \mathrm { m }$
B) $5.0 \times 10 ^ { - 6 } \mathrm {~N} \cdot \mathrm { m }$
C) $2.5 \times 10 ^ { - 6 } \mathrm {~N} \cdot \mathrm { m }$
D) $7.5 \times 10 ^ { - 6 } \mathrm {~N} \cdot \mathrm { m }$

Question

Quizplus · Accepted Answer

The torque on a current loop in a magnetic field is given by $\tau = nIAB \sin \theta$, where $n$ is the number of turns (1 in this case), $I$ is the current, $A$ is the area, $B$ is the magnetic field, and $\theta$ is the angle between the normal to the loop and the magnetic field. Here, $\theta = 60^\circ$, $I = 5.0 \, \mathrm{A}$, $A = 0.25 \, \mathrm{m}^2$, and $B = 1.2 \times 10^{-5} \, \mathrm{T}$. Thus, $\tau = 1 \times 5.0 \times 0.25 \times 1.2 \times 10^{-5} \times \sin 60^\circ = 7.5 \times 10^{-6} \, \mathrm{N} \cdot \mathrm{m}$.

A Flat Circular Wire Loop of Area 0.25 m20.25 \mathrm {~m} ^ { 2 }0.25 m2

A Flat Circular Wire Loop of Area $0.25 \mathrm {~m} ^ { 2 }$