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# Generators and Motors

## Electrical or kinetic energy can be generated using principles of magnetism.

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Generators and Motors

Changing magnetic fields passing through a loop of wire generate currents in that wire; this is how electric power generators work. Likewise, a changing current in a wire will create a changing magnetic field; this is how speakers and electric motors work.

Since only a changing flux can produce an induced potential difference, one or more of the variables in the equation must be changing if any emf is to be produced. Specifically, the following can all induce a current in the loops of wire:

• Changing the direction or magnitude of the magnetic field.
• Changing the loops' orientation or area.
• Moving the loops out of the region with the magnetic field.
Key Equations

emf=ΔΦΔtFaraday's Law of Induction\begin{align*} emf = -\frac{\Delta \Phi}{\Delta t}&& \text{Faraday's Law of Induction} \end{align*} Φ=NBA Electromagnetic Flux\begin{align*} \Phi = N \vec{B} \cdot \vec{A} &&\text{ Electromagnetic Flux} \end{align*}

The direction of the induced current is determined as follows: the current will flow so as to generate a magnetic field that opposes the change in flux. This is called Lenz’s Law. Note that the electromotive force described above is not actually a force, since it is measured in Volts and acts like an induced potential difference. It was originally called that since it caused charged particles to move --- hence electromotive --- and the name stuck (it's somewhat analogous to calling an increase in a particle's gravitational potential energy difference a gravitomotive force).

#### Example

To create a simple generator, you are holding a single coil of wire in place on a table. You hold a bar magnet directly above the center of the wire and move it toward the wire and away from the wire repeatedly to create a current in loop. (a) As you bring the bar magnet toward the loop, which direction does the current flow? (b) As you move the magnet away from the loop, which direction does the current flow?

(a): As you bring the magnet closer to the loop, the magnetic field will increase in strength thus increasing the magnetic flux going into the table through the loop. In order to oppose this change in flux, the induced current will need to create a magnetic field that will point out of the table through the loop. We can use the first right hand rule, starting with the direction of them magnetic field instead of the direction of the current, to determine that the current will need to move in the CCW direction.

(b): When you move the magnet away from the loop, the magnetic field will be decreasing thus decreasing the magnetic flux going into the table through the loop. The induced current will need to create a magnetic field that is also pointed into the table through the loop to oppose this change in flux. Again, we use the second right hand rule to find that the current must go in the CW direction.

### Review

1. How is electrical energy produced in a dam using a hydroelectric generator? Explain in a short essay involving as many different ideas from physics as you need.
2. When building a generator why not make it with almost infinite number of wire loops, since the emf is proportional to N the number of loops? What is the trade off, so to speak.
3. Explain how a motor works.
4. Explain in your own words why the generator in example 1 spins the same direction upon discharge.

1. A simple method would be to use the water to spin a turbine, which would in turn spin a loop of wire through a constant stationary magnetic field.
2. The field lines of your magnetic field only reach as far as they curl around.
3. If we bend a current-carrying wire into a loop in such a way that the two sides of the loop are at right angles to a magnetic field supplied by magnets, then the sides of the loop will experience forces in opposite directions which will create a torque to rotate the loop.
4. When we look at the direction that the current is flowing and the direction of the magnetic field, we find that the resulting force from these two physical vector quantities result in a torque spinning the generator in the same direction during which it was charged.

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