Make a Generator? You are shipwrecked on a deserted tropical...

Make a Generator? You are shipwrecked on a deserted tropical island. You have some electrical devices that you could uperate using a generalor but you have nu maguels. The eardis magnetic field at your location is horizontal and has magnitude 8.0 $\times 10^{-5} \mathrm{T}$ , and you decide to try to use this field for a generator by rotating a large circular coil of wire at a high rate. You need to produce a peak emf of 9.0 $\mathrm{V}$ and estimate that you can rotate the coil at 30 $\mathrm{rpm}$ by turning a crank handle. You also decide that to have an acceptable coil resistance, the maximum mumber of turns the coil can have is 2000 . (a) What area must the coil have? (b) If the coil is circular, what is the maximum translational speed of a point on the coil as it rotates? Do you this device is feasible? Explain.

Transcript

00:01 So here we'll review how a generator generates an electrical voltage and then look at some design parameters to see if they are feasible.

00:14 But basically a generator works off of faraday's law of induction.

00:22 And this law says that you can generate a voltage or an emf.

00:29 You can induce that voltage if you have a changing magnetic flux with time.

00:38 So we'll call magnetic flux phi, and it has to change in time.

00:45 And often the way you're generating the fluxes with a coil with a number of turns.

00:53 Magnetic flux, and here we're doing absolute value, but magnetic flux is a, product of a magnetic field vector dotted into an area vector.

01:07 So one of the most common ways to generate a voltage is using a coil that rotates in a magnetic field.

01:20 So that's what we're showing is that the coil area makes an angle with respect to the magnetic field.

01:28 And then there is a change.

01:31 Angle that changes with time.

01:37 That dot product goes as the cosine of theta between the magnetic field and the area.

01:45 If it is rotating, we get b .a.

01:49 Cosine of rotational velocity times time, angular velocity, or angular frequency.

01:58 Take your pick.

02:00 And the way that that flux changes in time looks like basically a sign with an omega out in front.

02:11 We'll take another absolute value.

02:14 And we can see then that we have a sinusoidally varying voltage that gets stronger when the coil is rotated faster.

02:28 So let's just kind of show how this thing would rotate.

02:33 It would rotate, flip over and over.

02:36 In the presence of the magnetic field.

02:41 And so finally, the voltage that you can generate with such a device, a generator like this, would be, and we'll talk just about the amplitude or the peak voltage would be omega -b -a times n, where n is the number of turns in your coil.

03:08 Or loops.

03:11 Okay, so let's take a look at a design parameter.

03:17 So we'll take a look at an example.

03:21 Let's say that the magnetic field is fairly weak, 8 times 10 to the minus 5 tesla.

03:31 Actually, that's fairly strong for the earth's magnetic field.

03:36 And let's say that you wanted to create a 9 -volt battery.

03:43 It's very common transistor voltage.

03:55 And also, all you have is a big pile of copper wire, let's just say that, and that you can wind it into a coil with about 2 ,000 turns and equals 2 ,000 turns...

Question

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