Why is the Angle Between the Normal to the Coil and Magnetic Field Important?

[Peter G.]

Hi,

So, I am learning about induced emf. I am having a hard time grasping the idea that we are interested in the angle between the normal to the plane of the coil and the magnetic field. In the standard illustration I actually understand it, but the following question confuses me.

We are dealing with the flux enclosed, so, shouldn't we want to find the cosine of the angle in the question attached as a picture?

Thanks!

 

[CFede]

Hi Peter, i think you are a bit confused.

As you say, we are interested in the flux enclosed, which means we are interested in that part of the magnetic field that goes through the ring rather than parallel to it.

Think of it this way. The flux is max when the magnetic field is perpendicular to the ring, in which case the angle in the figure would be Pi/2 (or 90 degrees). On the other hand, the fluz would be minimun (actually null) when the magnetic field is parallel to the ring, in which case the angle is 0.

Now, think about sine and cosine, when is the sine max and when is the cosine. Relate this to the explanation before.

Do you still think we should care about the cosine?

 

[Peter G.]

Oh I see! But I still didn't get the hang of this... Sorry. For example, look at the picture I attached. The question asks whether a vertical magnetic field, parallel to PQ and RS, would result in an induced emf as the window is opened at an angle of 90 degrees.

The answer is no.

Is it because:

Before the window is opened, the angle between the normal to the surface RQ and the magnetic field is 0, meaning max flux enclosed. After it rotates, the angle between the normal to the surface and the magnetic field is still 0. Does this mean no flux was cut?

Sorry for another similar question but I think if I can get around this example I will be done!

 

[CFede]

Maybe I didn't understand the problem, but... let's see...

When the window is closed, the normal to the surface points outside of the screen (to your face), and the magnetic field is pointing up, so the angle between those two is 90 degrees. As the window is opened this doesn't change, the angle between the normal and the magnetic field is still 90 degrees.

Now... this is going to be a bit confusing... opposite to what I said in the previous problem, when the angle between the normal and the magnetic field is 90 degrees, there is no magnetic flux. If you are careful, you'll see that, in the previous example, the angle shown is not the angle between the normal and the magnetic field, is the angle between a line on the surface and the magnetic field. So comparing both problems may be confusing since the angles you are considerin are not the same.

Now... back to the window problem, let's look at it from physics and mathematics:

From physics: The magnetic field is parallel to the window at all times, in other words, the magnetic field never goes through the window. By deffinition, the magnetic flux is the magnetic field that goes THROUGH a surface, per unit time, per unit area. Since in this case the magnetic field is paralel, it never goes through the surface and there is no magnetic flux.

From mathemathics: You are interested in the cosine here, since you are considering the angle between the normal and the magnetic field. The angle between the magnetic field and the window is always 90 degrees and cos(90)=0, so, again, there is no magnetic flux.

Remember, here we care about the cosine, in the previous example we cared about the sine, but that's only because the angles you are considering in each problem are different.

I hope this helps, but I get it may be confusing, if that's the case, feel free to ask again.

 

[Peter G.]

Thanks a lot again for the explanation! I got it now, don't worry. I had realized in the first question the angles were different and I learned that cos of theta is equal to sin of 90 - theta so it made sense.

Thanks once again!