Inductive Sensors for Traffic Lights
Induction is the electromagnetic concept of moving a conductor over a region of magnetic field in order to generate a current. It can also be applied to detect changes in electric fields, which is how it is very useful in creating sensors, such as those used in regulating traffic under traffic lights on major roads.
The Main Idea
The inductive sensors used in traffic sensors are very interesting pieces of equipment. They are the black loops of wire that you may have noticed on the surface of roads near an intersection. These loops of wire have a constant current flowing through them. When a large conductor, like the bottom of a car or truck, passes over the loop of wire, the electric field in the wire is altered and this change can be detected by an element like a transistor to signal a processor to change the light from green to yellow.
A Mathematical Model
The meat of the interaction between the conductor and the wire's magnetic field is that the conductor causes the magnetic field to change in the wire, and in turn causes the electric field to change. Thus, an important equation in modeling the emf generated at the bottom of the car when it moves over the wire loop is Faraday's Law: emf = d(phi)/dt, where phi is the magnetic flux, given by the integral of the dot product of magnetic field and the normal vector to the ground, with respect to dA (the area of the loop of wire).
Using Faraday's law, the emf generated in the conductor can also be used to find the electric field running through the wire loop, using a broader version of Faraday's Law in which the same emf calculated above is equal to the line integral of the dot product of the electric field in the wire and length vector around the wire.
A Computational Model
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