Rectangular Current Loop 1 2 3 4 5 6 A rectangular loop of wire with sides H = 2

Question

Rectangular Current Loop

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A rectangular loop of wire with sides H = 25 cm and W = 64 cm is located in a region containing a constant magnetic field B = 1.11 T that is aligned with the positive y-axis as shown. The loop carries current I = 188 mA. The plane of the loop is inclined at an angle = 27o with respect to the x-axis.

1)

What is x, the x-component of the magnetic moment vector of the loop?

A-m2

2)

What is y, the y-component of the magnetic moment vector of the loop?

A-m2

3)

What is z, the z-component of the torque exerted on the loop?

N-m

4)

What is Fbc, the magnitude of the force exerted on segment bc of the loop?.

N

Explanation / Answer

(A) |u| = IA = (188 x 10^-3) (0.25 x 0.64)

= 0.03 A m^2

u_x = - 0.03 sin27 = - 0.014 A m^2

(B) uy = 0.03 cos27 = 0.027 A m^2

(C) torque = u X B

= (-(0.014)i + 0.027j ) X ( 1.11j)

= - 0.015 k N -m

torque _z = - 0.015 N m

(D) Fbc = I ( BC x B)

= (0.188) [ (0.25)(-k) X 1.11j]

= 0.052 N

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