# Homework Help: Alternating current generator

1. Oct 15, 2016

### Drizzy

1. The problem statement, all variables and given/known data
https://goo.gl/wifHB3

{Image from: Electricity - Basic Navy Training Courses; NAVPERS 10622}

http://imgur.com/a/Pm2Rl

Here are two images, the one with colours is from my textbook. I don't understand why u is 0 when the thing inside is parallel with the ground and why is u at its max when the thing inside is vertical? I tried to google it and the first picture says differently

2. Relevant equations

3. The attempt at a solution

This is how I am thinking: When we go from point A to point B, the area gets smaller and that means φ gets smaller which should mean that u gets smaller not bigger. according to; u=-N dφ/dt

Last edited by a moderator: Oct 15, 2016
2. Oct 15, 2016

### Staff: Mentor

As you've noted the induced EMF is proportional to the rate of change of the flux within the loop. Why don't you set up a hypothetical scenario where you have a loop of some area A that is rotating as depicted. Write an expression for the the cross sectional area through which the field would pass as the loop rotates. That would give you a quantity proportional to $\Phi$. Find $d\Phi/dt$ to confirm or validate what's depicted in the images.

3. Oct 15, 2016

### Drizzy

Why is A 0 degrees? It should be 90

4. Oct 15, 2016

### lychette

If you look at the google image for the top diagrams you will see that the magnetic field is horizontal. So in effect both diagrams are the same

5. Oct 15, 2016

### Drizzy

I have one question, in which direction is the current flowing? I am thinking that the magnetic field is pointed down and the current is flowing in to the paper/book

6. Oct 15, 2016

### Staff: Mentor

Apply Lenz's Law.

7. Oct 15, 2016

### Drizzy

why cant I use the right hand rule?

8. Oct 15, 2016

### Staff: Mentor

You can, to determine the direction of the current that will satisfy Lenz's Law in this situation

9. Oct 15, 2016

### Drizzy

"You can see that the magnetic field lines run vertically. If the coil is also laid vertically, it lays in line with the field lines and don't cut them, so no current is induced. If no current is induced the voltage is 0."

How on earth can anybody explain that the coil in position A is lined up with the magnetic field lines?

10. Oct 15, 2016

### Staff: Mentor

The induced emf is NOT proportional the amount of flux passing through the loop, but to the rate of change of that flux. If the loop was not rotating there would be no emf induced at any angle it was positioned to.

That's why I suggested that you set up an expression for the flux with respect to the angle. Then the derivative of that with respect to time (i.e. the rate of change of the flux) will give you the emf. You will see that the cross sectional area exposed to the flux is proportional to a trig function of the angle...