Abstract The analysis of the two kinds of electric fields, namely the irrotational and non-conservative, is extended to electrodynamics, as exemplified by the high-frequency behavior of a parallel-plate capacitor and a radiating antenna. Since the concept of split electric fields still seems unfamiliar in some quarters, I will start back at square one by quoting…
Main Point The electric vector potential offers a means of determining the non-conservative component of a mixed stationary or quasi-stationary electric field. Background: magnetic vector potential Many readers will be familiar with the static magnetic vector potential ## \bf A = (\mu/4\pi) \int \bf j~ dv/s ## with ## \bf j ## = current (area)…
Introduction In a previous Insight, A New Interpretation of Dr. Walter Lewin’s Paradox, I introduced the fact that there are two kinds of E fields. One (Em) is generated whenever a source of emf is produced. The other (Es) is the electrostatic field. The Es field always terminates on free charges; the Em does not. …
Introduction Financial options — the right to purchase (call) or sell (put) stock or other assets at a fixed price on a future date — have been around for a long time. They are attractive to the option buyer because the buyer’s total risk is limited to the premium (price) paid for the option, unlike…
Introduction Much has lately been said regarding this paradox that first appeared in one of W. Lewin’s MIT lecture series on YouTube (see References [1]). This lecture was critiqued by C. Mabilde in a second YouTube video and submitted as a post in a Physics Forums thread (see References [2]). The latter cited a third…
Mixing vs. Beating: a brief history A long time ago I read a paper in the IEEE Proceedings recounting the history of the superheterodyne receiver. Overall it was a very interesting and informative article, with one exception: the author remarked that the modulation (or mixing) principle was nothing new and is already known to piano…
Introduction A subway tunnel could, in principle, operate without external energy (like electricity) if we assume zero friction everywhere. The train would descend, convert potential energy to kinetic energy, coast through a low point, then climb back up—all by exchanging potential and kinetic energy. Historical background What is the tunnel shape that minimizes travel time…
Mutual inductance and the coupling coefficient A commonly used formula for mutual inductance M between two nearby coils L1 and L2 is M = k√(L1*L2). This formula, however, assumes equal percentage flux linkages between the two coils. That requirement is often omitted in several references. Example: single-turn coil inside a long solenoid (Fig. 1) This…