A rectangular loop of wire of dimention 12 cm 25 cm faces a long, straight wire.
ID: 1471164 • Letter: A
Question
A rectangular loop of wire of dimention 12 cm 25 cm faces a long, straight wire. The two long sides of the loop are parallel to the wire, and the two short sides are perpendicular; the midpoint of the loop is 8.0 cm from the wire (see figure). Currents of 90 A and 60 A flow in the straight wire and the loop, respectively.
(a) What translational force does the straight wire exert on the loop? N
(b) What torque about an axis parallel to the straight wire and through the center of the loop does the straight wire exert on the loop? Nm
Please show your work. Thank you!
Explanation / Answer
A) let F be the force required
F = B*i2*L*sin(90) = B*i2*L
B is the magnetic field due to the straight wire = mu_o*i1/(2*pi*r) = (4*3.142*10^-7*90)/(2*3.142*0.08) = 2.25*10^-4 T
i2 = 60 A
L = 0.25 m
then F = 2.25*10^-4*60*0.25 = 33.75 N
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B) torque T = B*i2*A* = 2.25*10^-4*60*(0.25*0.12) = 4.05 Nm