## 20130405

### Presentation: generators

Look at this bicycle-powered generator. Just look at it. When the zombiepocalypse comes and civilization as we know it ends, would you be able to construct a generator from scratch?

In this presentation we will explain how generators work using right-hand rules of how magnetic fields exert forces on wires and loops. Later in a subsequent presentation we will explain how generators work using a magnetic flux approach.

First, "single-pass" generators, which can only be used once before having to be reset.

Consider a uniform magnetic B field, with uniform magnitude and direction (pointing into the plane of this page). A metal rod of length L is made to move at a constant speed and direction (to the right, in the plane of this page). As a result, the electrons in this metal rod will experience a force down along the rod (from either using the first right-hand rule to find the direction of the magnetic force on a (fictitious) positive charge, and reversing the direction of this force; or using the "left-hand rule"). As long as the rod is made to move through the magnetic field, the bottom end of the rod becomes negatively charged, while the top end of the rod becomes positively charged. The resulting difference in potential is a motional emf, and is the product of the rod's speed v and length L, and the magnitude B of the magnetic field. Thus moving a rod through a magnetic field makes the rod a battery!

Perhaps the ultimate proof of this principle was the Tethered Satellite System mission carried aboard the Space Shuttle, in which a 9.8 km wire was payed out as the Space Shuttle was moving through Earth's magnetic field. Actually much less wire was payed out before the tether broke, but there was a measured potential difference between each end of the tether.

Let's consider figurative depictions of "single-use" generators (more detailed consideration of how right-hand rules explain how these generators work will be covered in lecture). A rail generator has a rod made to move through a magnetic field, while the ends of the rod rest on rails, in order to make a complete circuit to take advantage of the motional emf generated in the moving rod (if the snowboard in this photo represents the rod, it would need to lie across both rails instead of sliding along one rail). In this sense this is a single-use generator, as you cannot indefinitely continue to slide the rod along the rail to generate a constant motional emf and current unless the rails are infinitely long in a magnetic field that is infinite in extent. Practically speaking, at some point you would need to stop the rod, and bring it back along the rails--this would still generate a motional emf, but with opposite polarity, in order to "reset" the system.

Another single-use generator is where a wire loop encounters the edge of a uniform magnetic field. As long as some part of the loop is still entering the magnetic field, there will be a motional emf that will produce current in the loop, until the loop is completely inside of the magnetic field. Practically speaking, at some point you would need to stop the loop after it has completely entered the magnetic field, and bring it back out of the magnetic field--this would still generate a motional emf and current, but with opposite polarity, in order to "reset" the system. Again more details of this generator using right-hand rules will be covered in lecture.

Second, "continuous" generators, that do not explicitly need to be reset in order to continuously provide motional emf and current.

A Faraday disk (or homopolar generator) consists of a metal disk that is cranked, while at least some part of it (or perhaps the entire disk) lies between the north pole and south pole of an external magnet. Wires are connected to the axis and the edge of the disk, and the constant potential difference of the motional emf can be measured with a voltmeter, or even made to generate current. No "resetting" required, so keep cranking!

More common generators have a coil that rotates between the north pole and south pole of an external magnet. This also generates a motional emf that can be measured with a voltmeter, or made to generate current, but the values of the motional emf (and current) will fluctuate over each cycle of rotation, or even change direction. Many circuit elements do not care which direction of current passes through them, or that the amount of current fluctuates very rapidly from this type of generator, so again, keep cranking.