(a) Calculate the magnitude of the magnetic moment of thisloop. | m | = A-m 2 HE

Question

(a) Calculate the magnitude of the magnetic moment of thisloop.

|m| = A-m2    

HELP:  Use the standard expressionfor the magnitude of the magnetic moment of a current loop (thisexpression applies to a loop of any shape provided it lies in aplane). Keep in mind that for the forces and torques on a currentloop, the relevant current is the net circulating currentN × I where N is the number ofturns and I the current per turn.

A spatially uniform magnetic field of strength B = 0.46T points in the +z direction. Let q denote the angle between the plane of theloop and the x-y plane. (See diagram.)

(b) What is the magnitude of the torque on the loop whenq = 0° ?

t = N-m    *
0   OK

(c) What is the magnitude of the torque on the loop whenq = 90° ?

t = N-m    

(d) Calculate the components (magnitude and algebraic sign) ofthe torque when q =27°.

tx = N-m   

ty = N-m    *
0   OK

A circular loop of radius a = 4.1 cm consists ofN = 20 turns. The current is I = 1.21 A per turn.When viewed looking down the x-axis, the current in thenearest portion of the loop is moving in the direction of the arrowshown in the diagram.

Explanation / Answer

(a) Calculate the magnitude of the magnetic moment of thisloop.

|m| = I.N.S = 6.23A-m2    

(b) What is the magnitude of the torque on the loop whenq = 0° ?

t = N-m    *
0   OK

(c) What is the magnitude of the torque on the loop whenq = 90° ?

t = B |m| = 2.87N-m    

(d) Calculate the components (magnitude and algebraic sign) ofthe torque when q =27°.

tx =B |m| sin q = 1.30N-m

ty = N-m    *
0   OK

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