A wire is pushed at speed v through a magnetic field.
The magnetic field points into the paper.
by Paul Doherty
Introduction
If you use a Genecon or other hand-cranked generator to charge a capacitor you might be surprised when you release the cranking handle to observe that it continues to turn in the same direction you were cranking it by hand. Particularly when you realize that as you were cranking you were charging the capacitor and when you stopped cranking the capacitor was discharging so that the current through the capacitor reversed direction.
Material
To Do and Notice
Turn the crank on the Genecon to charge the capacitor.
Stop turning the crank and observe that the handle continues to turn in the same direction.
What's Going On?
Inside the Genecon a wire is moved through a magnetic field when you turn the crank.
When the wire moves through the magnetic field a current is created which charges the capacitor.
When you stop moving the wire the current reverses direction and the magnetic field exerts a force on the wire in the same direction you were pushing it.
Consider a wire pushed to the right, in the x direction, through a magnetic field that points into the paper, in the y direction, A magnetic force is exerted on the charges that are free to move in the wire. The force is given by the Lorentz force law, F = q v x B. The vector cross product is upward in the z direction so positive charges are forced onto the + plate of the capacitor.
When you stop pushing the wire the capacitor discharges. Positive charges reverse their direction of flow. They flow from top to bottom of the vertical wire in the drawing, in the minus z direction. The Lorentz force on these moving charges is once again, F = q v x B . So that the force is in the direction in which the wire was being pushed. In the x direction.
To understand what's really going on consider the force exerted on the wire as you push it through the magnetic field.
The current of positive charges is in the z direction, when this current moves through a magnetic field in the y direction the Lorentz force on the current is F = q v x B .. So that the force is in the -x direction. While you are pushing the wire the magnetic force is opposing you. When you stop pushing the magnetic force reverses direction and pushes in the same direction you were pushing.
As you crank the Genecon the magnetic force on the wire you are turning opposes your motion, when you stop turning the crank the electric current reverses and the force reverses so that it now pushes in the same direction you were turning the crank.
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Scientific Explorations with Paul Doherty |
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15 April 2005 |