Why does the value of u change with the orientation of the loop?

[Drizzy]

Homework Statement

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

Homework Equations

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

 

[gneill]

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.

 

[Drizzy]

Why is A 0 degrees? It should be 90

 

[lychette]

Homework Statement

https://goo.gl/wifHB3
View attachment 107465
{Image from: Electricity - Basic Navy Training Courses; NAVPERS 10622}

http://imgur.com/a/Pm2Rl
View attachment 107466

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

Homework Equations

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

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

 

[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 into the paper/book

 

[gneill]

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 into the paper/book

Apply Lenz's Law.

 

[Drizzy]

why can't I use the right hand rule?

 

[gneill]

why can't I use the right hand rule?

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

 

[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?

 

[gneill]

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...