Equation for the EMF generated by a spinning magnet?

In summary, the conversation discusses an equation that calculates the electromotive force (EMF) generated in a coil when a magnet is spun near it. The equation, E = FNAω × 10-8 volts, includes variables such as field strength, number of turns, effective area of the coil, and angular velocity of rotation. The equation is compared to Faraday's law, E = N[ΔBA/t], and the question is raised about how to reconcile the differences in units. It is suggested that F may be a vector quantity, but its description and role in the equation are unclear.
  • #1
Wilfrid Somogyi
6
0
I have found an equation which gives the EMF generated in a coil when a magnet is spun near it, the equation is given as:

E = FNAω × 10-8 volts.

Where F is the field of the sample perpendicular to the axis of roation, N is the number of turns, A is the effective area of the coil and ω is the angular velocity of rotation.

Now this looks a lot like Faraday's law, E = N[ΔBA/t].

My question is, how do you get from Faraday's law to the first equation?

Assuming that when they say F is the field, they mean the strength of the field, I don't see how you can get the units to match up. Unless I'm mistaken and F is more than just the strength of the field and it is perhaps a vector quantity, but then what vector quantity is it and how is it desribed?
 
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  • #2
Update: I think I've sussed it, though if anyone can verify my mathematics that would be great.
derivation.jpg
 

1. What is the equation for the EMF generated by a spinning magnet?

The equation for the EMF (electromotive force) generated by a spinning magnet is given by: E = -N(dΦ/dt), where E is the EMF, N is the number of turns in the coil, and dΦ/dt is the time rate of change of the magnetic flux through the coil.

2. How does the number of turns in the coil affect the EMF generated?

The number of turns in the coil, represented by N in the equation, directly affects the magnitude of the EMF generated. As N increases, the EMF also increases, as there are more turns for the magnetic flux to pass through and induce a current.

3. What is the significance of the negative sign in the equation for EMF?

The negative sign in the equation signifies the direction of the induced current. It follows the right-hand rule, where the direction of the induced current is opposite to the direction of the change in magnetic flux.

4. How does the rate of change of magnetic flux affect the EMF generated?

The rate of change of magnetic flux, represented by dΦ/dt in the equation, is directly proportional to the EMF generated. This means that the faster the magnet spins, the greater the change in magnetic flux, and the higher the induced EMF will be.

5. Does the equation for EMF generated by a spinning magnet apply to all types of magnets?

Yes, the equation applies to all types of magnets as long as there is a change in magnetic flux. This includes electromagnets, permanent magnets, and even natural magnets like Earth's magnetic field.

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