Each of the 10 turns of wire in a vertical, rectangular loop carries a current o

Question

Each of the 10 turns of wire in a vertical, rectangular loop carries a current of 0.20 A. The loop has a height of 8.0 cm and a width of 15 cm. A horizontal magnetic field of magnitude0.045 T is oriented at an angle of ? = 65

Each of the 10 turns of wire in a vertical, rectangular loop carries a current of 0.20 A. The loop has a height of 8.0 cm and a width of 15 cm. A horizontal magnetic field of magnitude0.045 T is oriented at an angle of ? = 65 degree relative to the plane of the loop, as indicated in the figure below. Find the magnetic force on each side of the loop. Find the net magnetic force on the loop. Find the magnetic torque on the loop.

Explanation / Answer

B = 0.02*cos65 i + 0.02*sin65 j = 0.00845i + 0.01812j

a)
on top

y = 0.15(-j)
F1 = N*I*(yxB) = 10*0.045*0.2*0.15*sin25 = 0.00570535 k N.

y = 0.15 j

on bottom

F2 = N*I*(yxB) =10* 0.045*0.2*0.15*sin25 = 0.00570535-k N.


on left sides

z = 0.08k

F3 = N*I*(zxB) =10* 0.2*0.08*0.00845j +10* 0.2*0.08*0.01812-i = 0.0028992(-i) + 0.001352 j N


on right

z = -0.08k

F3 = N*I*(zxB) = 10*0.2*0.08*0.00845-j + 10*0.2*0.08*0.01812i = 0.0028992 i + 0.001352 -j N


b) Fnet = F1+F2+F3+F4

Net = 0


c) Torque = N*(uxB) = N*I*A*B*sin65 = 10*0.2*0.15*0.08*0.02*sin65 = 0.000435028 Nm

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