How Does Faraday's Law Explain Induced Current in a Changing Magnetic Field?

[pkossak]

I was wondering about the following problem:

You are looking down on a single coil in a constant magnetic field B = 0.9 T which points directly into of the screen. The dimensions of the coil go from a = 6 cm and b = 15 cm, to a* = 20 cm and b* = 19 cm in t=0.028 seconds. If the coil has resistance that remains constant at 1.7 ohms, what would be the magnitude of the induced current in amperes?

Now, I have the answer, and I was told how to get it. I used the formula I = (delta A*B)/(delta t*R)

What I was wondering was if someone could tell me what rule or law this formula came from? I can't figure out how to derive it from any of the formulas given in this chapter. Thanks a lot.

 

[Hootenanny]

This is an application of Faraday's law which is defined as the negative change is magnetic flux over time mulitplied by the number of turns on a coil and is defined mathematically thus;

$$emf = -N\frac{\Delta(BA)}{\Delta t}$$

You will also need Ohm's law;

$$V = IR$$

Can you go from here?

-Hoot

If you need a derivation of Faraday's law, you can do a search on the net or I'm happy to guide you through it here.

 

[kyle8921]

The formula you used, I = (delta A*B)/(delta t*R), is known as Faraday's law of induction. It states that the induced electromotive force (EMF) in a closed circuit is equal to the rate of change of magnetic flux through the circuit. In this case, the change in area (delta A) of the coil, multiplied by the magnetic field (B) and divided by the change in time (delta t) and the resistance (R), gives the induced current (I).

This law is a fundamental principle in electromagnetism and is often used in the study of electromagnetic induction and circuits. It was first discovered by Michael Faraday in the early 19th century and is one of the key laws that govern the behavior of electricity and magnetism.

I hope this helps clarify the origin of the formula you used and how it relates to Faraday's law. Keep exploring and learning about electromagnetism, as it is a fascinating and essential field in science.