# Current and Power From a Generated Voltage

When a conductor moves through a magnetic field, there will be a generated motional emf. This is one example of Faraday's Law and it arises from the magnetic force. The voltage generated in a length of wire, presuming that the entire length moves through a uniform field, is given below.

 Magnetic interactions with charge
 Magnetic force applications

If the velocity is perpendicular to the magnetic field then the generated voltage is given by the simple product:

## Generated voltage = emf = Velocity x B-field x Length

For a wire of length L = m = x 10^ m
moving with velocity v= x 10^ m/s
perpendicular to a magnetic field B = Tesla = Gauss
the generated voltage is V = x 10^ V.
If the angle between the velocity and magnetic field is degrees
the generated voltage is V = x 10^ V.

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Once you have calculated the generated voltage, a reasonable follow-up question is "How much current and power can I get from the generator?". Even though this would not be a practical generator geometry, it can serve as an idealization to discuss the principles of voltage generation by interaction with a magnetic field. Taking this simple geometry, the electric current in amperes generated from moving the wire through the magnetic field would be determined by the resistance of the circuit to which you have it connected, using Ohm's law, I = V/R. If you generated 10 volts and were connected to a circuit of resistance 1 ohm, the resulting current would be 10 amperes and the delivered power P=VI=10volts x 10 amps = 100 watts ( see the power relationship). But there is no such thing as a free lunch, and you would have to push harder to move the wire through the magnetic field at that speed - you are in essence trading mechanical energy of pushing for electrical energy out, always being limited by the conservation of energy principle. You would have to put in (at least) 100 watts of mechanical power of pushing to get 100 watts of electrical power out. Practical generators almost always use a rotating coil geometry, and large scale power generators use something like a steam turbine or a water turbine to turn a coil of wire in a magnetic field, getting voltage generated in both sides of the rotating coil.

If the generator above were connected to a circuit of resistance R = ohms,

the electric current would be I = V/R = amperes for velocity perpendicular to B.

The power supplied to the circuit would be P= VI = watts.

For the ideal case in which there were no losses, the required mechanical power P = Fv to push the wire through the magnetic field would be equal to the electric power. For the velocity stated above, the required force is given by

Ideal minimum required force:

F = P/v = newtons = pounds.

Index

Electromagnetic force

Magnetic field concepts

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