›› rand(foo); Adam Geboff


Speed of light in a vacuum

Electric fields travel at the speed of light - a constant 299,792,458 meters per second regardless of wavelength.  However, this fact is only true for the ideal case where the waves are traveling through vacuum away from any other charge sources.  In non-ideal situations, where an electric field is traveling through another medium, the speed of the field is slowed.  But how slow?

In order to understand how different mediums effect an electric field's velocity, we first need to understand why the speed of light travels at the velocity it does in that idealized case.  The first part of this multi-part series is going to discuss the general form of the wave equation followed by a derivation of the speed of light in vacuum.


The Hall effect

Since i have found a position with Carnegie Mellon, i now have the time to reflect on my job search and more to the point, the interviews.  While most of the time was spent discussing the experience listed on my resume, the question i remember hearing the most was if i could explain what the Hall effect is.  Now, i have designed circuits leveraging Hall effect sensors in the past - in motor controllers as angular position sensors, in magnetic switches, and in scroll wheels as linear position sensors, but i never took the time to dig in and understand how the sensors worked.  For all i cared it could have been voodoo, black magic, or a combination of the two - one way or another the sensor is able to tell me where it is in relation to a nearby magnetic field.  That only gets you so far, so i guess it's time to demystify these little ICs.

What is the Hall effect:
The Hall effect, named after the scientist who first detected it Edwin Hall, is the opposing force a flow of charge carriers (current) induces to cancel out a Lorentz force acting upon it.  This opposing  forces is equal in magnitude and opposite in sign to the Lorentz force in order for the steady state net force on the carries to be zero, satisfying Newtons 3rd law.  This answer requires a basic understanding of the fundamental laws of classical electromagnetic fields - Maxwell's equations, and  the Lorentz force where Maxwell's equations describe how moving charge carriers induce EM fields and the Lorentz force is how EM fields effect moving charge carriers.

How to leverage the Hall effect:
One generally uses Hall effect sensors to sense the position of a magnet, or the magnitude of a current.  There are 3 main types of position sensors - binary, linear and radial.  For each, it is assumed that there is a magnetic field (generally generated by a magnet) that is a part of the component you want to sense the position of, in a location where it will pass over the sensor's active area.

  • For a binary sensor, it will switch logic states when the active area is in proximity of a north or south pole (axially magnetized).
  • For a linear sensor, it will give you an analog or multiple bit digital output corresponding to the distance the active area is away from a north or south pole.
  • For a radial sensor, it will give you an analog or multiple bit digital output corresponding to the angle at which the north/south pole is to the active area.  Radial sensors require a diametrically magnetized magnet persistently centered on the sensors active area.
  • For current sensing, the Hall sensor's active area is placed perpendicularly to the currents induced magnetic field and will output an analog or multiple bit digital signal corresponding to the current's magnitude.

How do Hall effect sensors work:
Internal to the IC, there is a rectangular plate that a small current travels through in the y-direction, with voltage sensing circuitry connected across the plate in the x-direction.  While there is no external magnetic field and therefore no Lorentz force, the current travels linearly through the plate and no voltage difference can be sensed at the sides of the plate.  However, in the presence of a magnetic field perpendicular to the current flow (through the large surface of the plate in the z-direction), an electric field is formed called the Hall field which when integrated across the length of the plate gives you the a voltage differential called the Hall voltage.