A coil of wire consisting of 40 rectangular loops, with width 16 cm and height 3

Question

A coil of wire consisting of 40 rectangular loops, with width 16 cm and height 30 cm, is placed in a constant magnetic field given by = 0.040T + 0.200T . The coil is hinged to a fixed thin rod along the y-axis (along segment da in the figure) and is originally located in the xy-plane. A current of 0.260 A runs through the wire. What are the magnitude and the direction of the force, , that exerts on segment ab of the coil? magnitude Fab = direction What are the magnitude and the direction of force, , that exerts on segment be of the coil? magnitude Fbc = direction What is the magnitude of the net force, Fnet, that exerts on the coil? What are the magnitude and the direction of the torque, , that exerts on the coil? magnitude tau = direction

Explanation / Answer

a) Fab = NI L x B = 40*0.26*(0.16 i)x(0.4 i + 0.2 k) = - 40*0.26*0.16*0.2 j= 0.3328 N in - y direction

b)Fbc = NI L x B = 40*0.26*(0.3 j)x(0.4 i + 0.2 k) = - 0.1248 k + 0.624 i

|Fbc| = sqrt(0.1248^2 +0.624^2) = 0.6363 N direction = -tan^-1(0.1248/0.6363)

c) Fnet = 0 N

d) tau = F x w = (-0.1248 k + 0.624 i)*0.16 i= 0.019968 N-m in +y direction

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