Understanding Inductance Diagrams and EMF Generation in Electrical Systems

[hellogirl88]

I have a few statements that I have to discern whether they are true or false and I am down to my last guess and am completely stumped.

1. No EMF will be generated by a coil rotating inside a magnetic field if the axis of rotation is perpendicular to the field.

2. In an electrical generator, the generated peak voltage is proportional to the angular velocity of the coil in the field.

3. For a loop moving inside of a constant magnetic field, the EMF is proportional to its velocity.

4. EMF can be generated by rotating a coil inside of a magnetic field, which increases with time.

Originally I thought 1 and 2 were false and 3 and 4 were true, but I was wrong. Can anyone figure this out?

 

[Gib Z]

Okay so let's try work through these. To do these, we are going to need to be familiar with Faraday's Law of Induction, so read up in your textbook about that first! Just so we know, reply back here exactly why Faraday's Law is.

1. Try visualize it, draw a diagram, or put your hands in the place of some of the objects. Faraday's Law says an EMF is induced if there is a change in flux through the coil, ie if there is a change in the number of flux lines going through the coil. If the coil rotates on an axis perpendicular to the field, can you see if there is going to be more or less flux when the coil is completely vertical than when it's horizontal?

2. Well, what creates the voltage in a generator? Does the angular velocity of the coil in the field change this?

3. This one should really be more specific, the answer depends on how the loop "moves" in the field. Can you see why?

4. This statement follows quite simply from the Principle of Induction, though the "which increases with time" tacked on the end doesn't seem to make sense. If it means the strength of the field is increasing with time, it adds a new element to the answer but doesn't change the overall result.

 

[nlightner]

I can confirm that statement 1 is true. This is because when the coil's axis of rotation is perpendicular to the magnetic field, the flux lines do not cut through the coil, resulting in no EMF being generated.

Statement 2 is also true. This is because the generated EMF is directly proportional to the rate of change of magnetic flux, which is dependent on the angular velocity of the coil in the field.

Statement 3 is false. The EMF generated in a loop moving inside a constant magnetic field is actually proportional to the rate of change of the magnetic flux, which is dependent on the velocity of the loop, not its velocity.

Statement 4 is true. This is because when a coil is rotated inside a magnetic field, the magnetic flux through the coil changes, resulting in an induced EMF. This EMF can increase with time if the rotation speed of the coil increases.