A small current loop creates a dipolar magnetic field, which wedescribe by its m

Question

A small current loop creates a dipolar magnetic field, which wedescribe by its magnetic moment
m = Ia , where I is the current in the loop and ais the vector area, which is a vector pointing
perpendicular to the loop in the direction dictated by theright-hand rule and with a length proportional to
the area of the loop.

a. What is the magnetic moment of a circular loop of wire withradius 1cm and current 1A?

b. If instead of a single loop, we loop the coil around 10 times,what is the resulting magnetic
moment?

c. How many loops of wire with radius 1cm and current 1A would oneneed to replace the permanent
magnet in the problem above?

Explanation / Answer

1..we know that m=nia              (n=1) or, m= i r2 orm=1*3.14*10-4               (since 1cm=10-2) or, m=3.14*10-4 Am-2 -------------------------------1 2.   m=nia       m=10*3.14*10-4           (since ia=3.14*10-4)------------- 1       m=3.14*10-3Am2 ------------------------------------------2 2.   m=nia       m=10*3.14*10-4           (since ia=3.14*10-4)------------- 1       m=3.14*10-3Am2 ------------------------------------------2

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