A wire 1.80m long carries a current of 26.9 mA when it is connected to a battery

Question

A wire 1.80m long carries a current of 26.9 mA when it is connected to a battery. The whole wire can be arranged as a single loop with the shape of a circle,square,or an equilateral triangle. The whole wire can be made into a flat,compact,circular coil with N turns.
Calculate the magnetic moments in each case. In particular, can its magnetic moment go to infinity? Can its magnetic moment go to zero? Does its magnetic moment have a well-defined maximum value If so, identify it. Does it have minimum value?

Explanation / Answer

a)

magnetic moment

u =NIA

For Single turn circle N=1

radius of circle

r=L/2pi =1.6/2pi =0.2865 m

Area of circle

A=pi*r2= pi*0.28652

A=0.2578 m2

Magnetic moment

u=NIA =1*0.0269*0.2578

u=6.94*10-3 A-m2

Single turn square N=1

Length of each side

L=1.8/4 =0.45 m

A=L2 =0.452 =0.2025 m2

Magnetic moment

u=1*0.0269*0.2025

u=5.45*10-3 A-m2

Single turn traingle N=1

Length of each side of equivlateral traingle

L =1.8/3 =0.6 m

Area of equivalateral traingle

A=sqrt(3)/4*L2 =sqrt(3)/4*0.62

A=0.1559 m2

Magnetic moment

u=1*0.0269*0.1559

u=4.2*10-3A-m2

e)

u=6.94*10-3 A-m2

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