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## AP®︎/College Physics 2

### Unit 5: Lesson 4

Magnetic flux and Faraday's law# Faraday's Law for generating electricity

How Faraday's Law is used to generate electricity in turbines.

## Want to join the conversation?

- Can anyone explain me about the sinusoidal behaviour of the induced emf in an ac generator?

I am unable to understand why the emf curve goes below the x-axis as the armature coil rotates. E.M.F is on y-axis and direction of magnetic field is on x-axis.(5 votes)- circular motion gives you simple harmonic motion, and simple harmonic motion graphs as a sinusoid

watch

http://tube.geogebra.org/student/m42907(7 votes)

- Do we have an exact formula to count the change in flux if we rotate the loop? Thx.(3 votes)
- If I get your question right, you need to work out the 'rate of change of area' as the loop turns. Is this what u mean?(5 votes)

- why does the direction of current in generator change. And what would happen If instead of slip rings we used split rings?(2 votes)
- Hello Harshulsurana,

The direction of current is a function of the relative motion of the conductor and the magnetic field. You can visualize this using the right hand rule.

Slip rings give us an AC machine.

A commutator (split rings) give us a DC machine

Regards,

APD(4 votes)

- i cant understand why the electromagnetic curve goes below the x axis as the armature coil rotates. electromagnetic is on y-axis and direction of the magnetic field is on x axis(2 votes)
- what are the avantages of having AC current? Or do we usualle try to convert this into DC?(2 votes)
- A really short answer would be that it´s more energy efficient and easier to generate, and the process for transforming AC is really easy(not so the other way around).For really know the reasons of this , you have to go deeper in electronics. :)(2 votes)

- Can some one explain in detail the differences between AC and DC. I mean I know that one displays sinusoidal behaviour and can travel over longer distances without getting disturbed but can someone explain the why and how of that or direct me somewhere where I can learn about that .

Thanks for the help !(2 votes)- Hello VIshnu,

I've been working on answering questions such as this. Please see my YouTube video at

https://www.youtube.com/watch?v=kQP7JW1H5zM

Here I explain DC and AC as mathematical function and give examples of where each type of power is found in an electrical power system. It also introduces the technology that allows you to convert between the two types.

At some point in the future I hope to do a video on DC transmission where you will see that DC is king for long distance transmission.

Regards,

APD(0 votes)

- When rotating the loop Sal says that the component of the Magnetic Field is going to increase, How?(2 votes)
- At1:44the picture on the left shows a loop of wire turning in a constant magnetic field. As the loop rotates the number of flux lines enclosed within the loop changes. This change in flux induces a voltage in the loop.

Keep spinning! APD(0 votes)

- Is the triangle symbol a greek letter?(1 vote)
- Yes. Δ is the Greek capital letter "Delta". When it appears before any variable, it means "change in ...". So in this video, for example, there is Δt, and that means "change in time". You always calculate the change by subtracting the initial value from the final value, so Δt = tf - ti(2 votes)

- where's the limit of increasing number of loops to augment the motor strength?(2 votes)
- Increasing the number of loops increases the EMF of the coil. Increasing the EMF of the coil will increase the amount of energy needed to make it spin. Windmills are designed to work efficiently, with coils and magnets matched to where the windmill will reach peak power output, but not to where it exceeds peak power output. The wings on windmills should only spin so fast as to not exceed the maximum current allowed through the system, limitations of the system could include its electrical wiring and components, also it's mechanical and structural components. So, the limit of loops really comes down to the specific generator, although there may be a theoretical limit based on magnet size. Approaching that limit would more than likely require too much energy to rotate at any speed to produce current.(0 votes)

- If the turn ratio of a transformer is 10. What does it mean?(2 votes)
- Hello Muhammad,

Turns ratio is literally a ratio. Recall that a transformer is composed of two coils of wire. Each coil consists of some number of "turns" around the transformer's core.

Suppose a transformer that has a turns ratio of 1 to 10. Let the first coil consist of 500 loop of wire. The second coil will have 5000 turns.

This turns ratio is very important as it also describes the voltage into and out of the transformer. In this example if the input voltage is 100 VAC the output voltage is 1000 VAC.

Please leave a comment below if you would like to continue the conversation.

Regards,

APD(0 votes)

## Video transcript

- [Voiceover] We're already looked at Faraday's law in some detail. It showed us that if we have some loop of conductor and we have a change in magnetic flux over
time through the surface defined by that loop, it's going to induce an EMF through that loop which will cause a current to start to
circulate through that loop and that current, of
course, will be dependent on the actual resistance of the conductor. And there's many ways
that we've already seen of having a change in magnetic flux. One, you can have a change
in the magnetic field. It could be a change in its magnitude and, or it's orientation. You could have a change in the shape of the actual loop of conductor. If its area increases or decreases, that will change the flux. Remember, the flux is just your, the component of the magnetic field that is perpendicular to the surface. If you took the average of that times the area of the surface. And then the other way that we're going to study in this video is
inducing an electromotive force by changing it, not the shape of the loop and not the magnetic field but by changing the orientation of the loop. And in particular, we're
going to have the loop rotate. So let's think about this.
So I have this loop here. It's connected to this axle
and I'm going to rotate it in a, I'm going to rotate
it in a clockwise direction through this constant magnetic field. You can see it's constant. All of the magnetic field vectors I've just sampled'em at
different points in the field. They're all pointing straight
up and I've drawn them so that they all have the same magnitude. Now we'd appreciate is as we rotate this, the angle between the magnetic field and the surface is changing
and right from this point, as we rotated this clockwise direction, the component of the magnetic field that is perpendicular to the
surface is going to increase. Now what am I talking about? Well, let's look at it
from this point of view. Let's look at it from the point of view of the actual loop of wire,
so from this point of view the magnetic field is at some angle. I can draw that angle here
so, you know, whatever angle, it's a little hard to see,
whatever angle this is, we could say that is that angle here and as we rotate the
entire loop, it's attached to some type of an axle here,
in a clockwise direction. What is going to happen to this angle? Well, after let's say delta
T, let's say we're just rotating it a constant
rate, we're going to have the magnetic, so after
we've rotated a little bit, the magnetic field of vector is going to look something like that. So it's the component
that is perpendicular to the surface was what
we care about for flux, it's going to go from being
like this, it's gonna go from being like that to going to being, to being like this, to being like this. So at least for this
point of the rotation, for this point of the rotation till we get to the flat, until we
get to the flat point, until we have our loop
being completely flat, the component of our magnetic field that is perpendicular is going to increase which is going to have,
so we're going to have an increase in flux over that time. So if we have an increase
in flux over that time as we rotate up, at least
until we get to the flat point, what is going to happen? Well, we're going to induce a current and then we just have to think about what is the orientation of the current? So we want to have a current that will induce a magnetic field that will go against the change
in flux so the current should induce a magnetic field that is, if our flux, at least for
that part of the rotation is increasing in the upwards direction, if we're from the point
of view of this loop, then we need to create a magnetic field that is acting against that. So magnetic field that
is acting against that or we need to, we're
ready to induce a current that induces a magnetic field that acts against that change in flux. So, how do I, what type of current would induce a magnetic field like that? So I'll just use the
right-hand rule, my fingers would go in the direction of these, of the magnetic field, so my fingers and I have to use my right hand, so my fingers are gonna
go in that direction, so my right hand, my thumb, my thumb would go in this direction. So that is going to be the direction of the current that is induced. So the whole point of me showing you this, is that there's multiple ways to have a change in magnetic flux and there's multiple ways to induce a current. And this one is particularly interesting because it lets you or we
can start to think about, wow, I could turn, I could
turn a mechanical rotation into an induced current and
this is, this basic principle although they wouldn't use
such a simple loop like this, is exactly how electric generators work. They're actually, in some ways, the reverse of an electric motor. An electric motor has a current that causes something to rotate. Here, we're having something rotate causing a current to
form and that's actually what we have happening when you look at something like windmills or when you look at hydroelectric generators. Right over here, this windmill, the wind is going to cause these
blades to turn around and then inside, inside
of this little place right over here, you're going
to have a more fancy version of this rotating which is
going to induce a current. The magnetic field isn't
going to be exactly like this. It's going to be a more
sophisticated mechanism but it's the same underlying principle. It's just Faraday's law at work. Same thing with hydroelectric generator, you're using the potential energy of the flowing water to turn an axle and then that helps us
generate electricity by the exact same principle.