Answer to Question #212059 in Electricity and Magnetism for Mickie

Question

A rectangular loop of wire with sides H = 26 cm and W - 50 cm is located in a region containing a constant magnetic field

B - 0.87 T that is aligned with the positive y-axis as shown. The loop carries current I = 387 mA. The plane of the loop is

inclined at an angle 8 - 33° with respect to the x-axis.

1) What is My the x-component of the magnetic moment vector of the loop?

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

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

4) What is Fpc, the magnitude of the force exerted on segment bc of the loop?.

5) What is the direction of the force that is exerted on the segment be of the loop?

Answer 1

$M=IA=IHW,$

1)

$M_x=-IWH\sin \alpha=-27.4~mA\cdot m^2,$

2)

$M_y=IWH\cos\alpha=42.2~mA\cdot m^2,$

3)

$T_z=-\mu B\sin \alpha=\mu_xB=-23.8~mN\cdot m,$

4)

$F_{bc}=IHB=87.5~mN,$

5)

along the negative y-direction.