Electromagnetic Induction

Question

A 16-cm-diameter circular loop of wire is placed in a 0.50-T magnetic field. (a) When the plane of the loop is

perpendicular to the field lines, what is the magnetic flux through the loop? (b) The plane of the loop is rotated until it makes a 42° angle with the field lines. What is the angle T for this situation? (c) What is the magnetic flux through the loop at this angle?

Answer 1

Hi Aira!

Let's stop and think about the idea of "flux" in general. We learned earlier about "electric flux" in the context of Gauss' Law, namely the Electric Field integrated over the surface of our 3-D Gaussian surface.

Magnetism, however, is a bit different. We know from Maxwell's Equations that    . All this says is that over a 3-D surface, the same integral of the magnetic field is 0 

This tells us that there are no magnetic monopoles!

We return now to the question at hand concerning 2-D magnetic flux. In this case, we're taking a circular loop of wire and asking how many B Field lines make it through?

In the first case (plane of loop is perpendicular to field), the flux is just B*A = 0.50 * (pi).08^2 = 0.01 Tm^2

b) I believe this is asking for the angle between the normal of the circular plane and the field lines given the angle between the plane itself and the field. In this case, we would merely take 90 (the normal is orthogonal to the plane) - 42 = 48 degrees.

c) Here, we want the inner product (dot product) of the normal and the field, evaluated across the circular surface. This is simply B * A * cos(48) = 0.0067 Tm^2

Hope this helps!