Lecture 107: From Electrostatics to Electrodynamics: Understanding Electric Current and Ohm's Law

In this video, I transition from electrostatics to electrodynamics by introducing the concept of electric current. I begin with a phenomenological exploration of electric conduction, explaining how free electrons in a wire subjected to an electric field experience acceleration. However, due to scattering from ions in the conductor, these electrons settle into a slow, constant drift velocity, much like a lead-footed driver navigating a road filled with stop signs. I calculate the drift velocity for a copper wire carrying a current of 1 A, revealing that it is more than ten orders of magnitude slower than one might intuitively expect.
In the second half of the lecture, I delve into the microscopic origins of electric conduction by modeling an electron moving in a viscous fluid under the influence of a constant electric field. I relate the relaxation time of the velocity to the time between collisions and the mean free path of the electrons. Finally, I equate the drift velocity equation from the first part of the lecture with the equation derived from the microscopic model to arrive at Ohm's law. This law states that the voltage drop across a conductor is proportional to the current, with the proportionality constant being the resistance. Through this discussion, viewers gain both a macroscopic and microscopic understanding of electric conduction and its fundamental laws.
Problem set for this lecture is here:
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