This video is about the induced EMF in a coil that is moving through a magnetic field.
We'll examine three different moments as the coil moves through the field.
First, as the coil enters the field. Second, as the coil is entirely inside the field
and is moving through the field. And finally, as the coil is leaving the field.
Let's see what happens as the coil starts entering the field.
Here, we can take two different approaches.
First, let's use Fleming's right hand rule.
If you would like to refresh how this rule works, feel free to watch video 11.1.1
titled induced electromotive force. So in order to find the direction of the induced current,
point your thumb in the direction of the conductor's motion, so to the right,
point your index finger in the field direction, so into the screen or page.
And if you have done this correctly, your middle finger should show the
direction of the induced current, which here is upwards.
This is the current induced at the right end of the coil, so here.
Since the left end of the coil has not yet entered the magnetic field,
there is no current induced in this section of the coil.
Since the coil is moving horizontally, and the two longer sides of the coil are horizontal,
logically, there is no induced current in these two sides either.
Since the coil can be considered as a closed circuit, the current that is induced at the right
end of the coil will be able to flow around the coil. Therefore, there is an anticlockwise
current in the coil, so there is also an induced EMF in the coil.
Another approach that we can take to show that there is an induced EMF in the coil
is to use Faraday's law. Here is the equation that expresses this law.
To revise how this law works, feel free to watch the previous video.
This law tells us that a changing magnetic flux causes an induced EMF.
As the coil is entering the magnetic field, magnetic flux through the coil is increasing.
Since there is a change in magnetic flux, there is an induced EMF in the coil.
Next, let's see what happens as the coil is passing through the field.
Once again, we can use Fleming's right hand rule to find the direction of the induced current.
I won't go through the steps here again, but the big difference in this case
is that since both the right side and the left side of the coil are now moving through the field,
there is an induced upward current at both ends of the coil.
Just as before, there is no induced current in the horizontal sections of the coil,
and you can imagine that the two upward currents at the two ends cancel each other out,
therefore no current flows around the coil. Of course, this also means that there is no
induced EMF in the coil. Let's confirm this using Faraday's law.
As we said earlier, there must be a change in the magnetic flux through the coil
in order for an EMF to be induced. As the coil is moving inside the magnetic field,
assuming that we have a uniform magnetic field, the number of field lines that enter the coil
is the same as the number of field lines that leave the coil.
As a result, the number of field lines inside the coil does not change,
therefore the magnetic flux through the coil does not change.
Since there is no change in magnetic flux, there is no induced EMF.
Finally, let's see what happens as the coil is leaving the field,
once again starting with Fleming's right hand rule.
As the coil is leaving the field, the right end of the coil has already left the field,
so here no current is induced, while since the left end of the coil is still moving in the field,
here we have an induced current upwards.
Once again, there is no induced current in the horizontal sections,
so as the coil is leaving the field, there will be a clockwise current in the coil.
Of course, as a result, there is also an induced EMF in the coil,
which we can confirm by using Faraday's law.
This time, the magnetic flux through the coil is decreasing,
and since this is a change in magnetic flux, there will be an induced EMF in the coil.
Examining the Faraday's law equation, we can also confirm that the sign of the induced EMF
will be different when the coil is entering the field and when the coil is leaving the field.
So for instance, if the induced EMF is taken to be positive when the coil is entering the field,
it will be negative when the coil is leaving the field.
This completes our discussion of induced EMF in a coil moving through a magnetic field.
In the next video, we'll discuss what happens when a coil is turning in a magnetic field.