What is the magnetic field at the center of coil 1 for a current I=I0cos(wt)? As

Question

What is the magnetic field at the center of coil 1 for a current I=I0cos(wt)?

Assuming that the magnetic field is uniform within the area of coil 2, what is the magnetic flux passing through a single turn of coil 2 due to coil 1?

What is the EMF generated in coild 2 due to the changing current in coil 1?

The mutual inductance between coil 1 and 2 is defined by the relation EMF2=-M(dI1/dt). Find M21 in terms of some or all of the variables N1,N2,r1,r2.

We a coil creates a current that creates a magnetic field. Background: We have learned that EMF across have also learned that changing magnetic flux through a coil creates an EMF in that coil. This means that fed into one coil causes an oscillating EMF, in the second coil. This is the basis for a useful device called a transformer We will work through the relationship between currents and EMF's in two coils for a special case as sketched to the right. The large coil in the sketch is Coil I. It has N1 turns and radius ri. The smaller coil is Coil 2 with N2 turns and radius r2. % 1) What is the magnetic field at the center of coil 1 for a current of 1() = 10 cos ar ? 2) Assuming that the magnetic field is uniform within the area of Coil 2, what is the magnetic flux passing through a single turn of coil 2 due to coil 1? 3) What is the EMF generated in coil 2 due to the changing current in coil 1? 4) The mutual inductance between coil 1 and 2 is defined by the rela dl . Find M21 in dt 21 terms of some or all of the variables M, No, Pi, and r

Explanation / Answer

1) B = u0 N1 I1 / (2 r1)

N = (u0 N1 I0 / 2 r1) cos(wt)

2) magnetic flux = B.A

= (u0 N1 I0 pi r2^2 / 2 r1) cos(wt)

3) e = d(flux)/dt = -(u0 N1 N2 I0 pi r^2 w / 2 r1) sin(wt)

4) M21 = u0 N1 N2 pi r2^2 / 2 r1

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