How Is the Magnetic Moment Calculated in a Solenoid-Wire System?

[eestep]

Homework Statement

A solenoid runs in z direction through x-y plane. As it passes through plane current is running counter-clockwise with an amount of I(t)=2.3 A/s²t² (increasing over time counter-clockwise). Also, n=7 x 10⁴/m for solenoid. A wire shaped as a square with sides of 1.2 meters with a equilateral triangle on top side is placed in x-y plane, in solenoid. Resistance of wire is 10 ohms and N=4. At t=23.9 seconds, what is magnitude, in Am², and direction of magnetic moment of wire? Indicate negative z direction with a negative sign. Answer is -72.19.

Homework Equations

$$\mu$$=NIA

The Attempt at a Solution

$$\mu$$=4(2.3(23.9)²))(1.2m²+1/2*1.2m*1.04m)

 

[nilesh_pat]

\mu=72.19 Am2The direction of the magnetic moment is negative z direction since it is counterclockwise. So, -72.19 Am2