Misconceiving Mutual Inductance Coefficients
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. This...
View ArticleLearn About Energy Gained by Charge in an Electrostatic Field
I have seen this question being asked frequently on here. A lot of students have a bit of an issue in understanding why, if an electron is placed in a field with potential V, that the energy gain after...
View ArticleAcoustic ‘beats’ from Mismatched Musical Frequencies
In late high school physics courses and first-year university courses, the phenomenon of acoustical ‘beats’ is often covered. This is an interesting phenomenon, but it is usually only skated over,...
View ArticlePermanent Magnets Explained by Magnetic Surface Currents
Introduction: The purpose of this Insight is to explain permanent magnets in a way that is in agreement with advanced textbooks on the subject, and that emphasizes the results in these textbooks...
View ArticleA New Interpretation of Dr. Walter Lewin’s Paradox
Much has lately been said regarding this paradox which first appeared in one of W. Lewin’s MIT lecture series on ##{YouTube}^{(1)}##. This lecture was recently critiqued by C. Mabilde in a second...
View ArticleAre Magnetic Field Lines Real?
We recently had a question in the relativity forums that mentioned the behavior of magnetic field lines and reminded me of my own confusion at school about what magnetic field lines actually were. You...
View ArticleWhat is the Double Slit? A 5 Minute Introduction
Definition/Summary The double-slit is a simple configuration used to demonstrate interference effects in waves. Equations At distances that are large compared to the spacing between the slits (i.e. the...
View ArticleMaxwell’s Equations in Magnetostatics and Solving with the Curl Operator
Introduction: Maxwell’s equation in differential form ## \nabla \times \vec{B}=\mu_o \vec{J}_{total}+\mu_o \epsilon_o \dot{\vec{E}} ## with ## \dot{\vec{E}}=0 ## comes up quite frequently in...
View ArticleRelativistic Treatment of the DC Conducting Straight Wire
Introduction The direct-current-conducting infinitely long wire is often discussed in the context of relativistic electrodynamics. It is of course a completely academic discussion since for the typical...
View ArticleHow to Recognize Split Electric Fields
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...
View ArticleAre Electromagnetic Waves Always Transverse?
In this insight, we shall endeavor in the realm of classical electrodynamics and examine whether EM waves are always transverse. We shall make use of Jefimenko’s equations and Poynting’s Theorem and...
View ArticleSplit Electric Fields in Electrodynamics: Capacitor and Antenna
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...
View ArticleHow to Use Duality in Computational Electromagnetic Problems
Some weeks ago I happened across a post that caught my eye. Dale asked a question about the number of photons in an electromagnetic field. His question was answered in full but what caught my attention...
View ArticleA Numerical Electromagnetic Solver Using Duality
In the previous insights article (How to Use Duality in Computational Electromagnetic Problems), I covered some uniqueness theorems for the Riemann-Silberstein vector, ##F=E+iB##, for time-harmonic...
View ArticleSymmetry Arguments and the Infinite Wire with a Current
Many people reading this will be familiar with symmetry arguments related to the use of Gauss law. Finding the electric field around a spherically symmetric charge distribution or around an infinite...
View ArticleHow to Model a Magnet Falling Through a Solenoid
Introduction Modeling a magnet realistically is a task best done numerically. Even the simplified model of two separated disks with uniform surface magnetization ##\pm~\sigma_M## involves elliptic...
View ArticleHow to Model a Magnet Falling Through a Conducting Pipe
Introduction In an earlier article, we examined a magnet falling through a solenoid. We argued that the point dipole model can account for the basic features of the induced emf across the solenoid...
View ArticleA Physics Misconception with Gauss’ Law
Introduction It is relatively common to see the following type of argument: The surface area is ##A## and the enclosed charge is ##Q##. The electric field strength on the surface is therefore ##E =...
View ArticleThe Poor Man’s Milli-Ohm Meter
Introduction In a previous article on measuring battery internal resistance, a simple technique for low-resistance measurement was outlined. In this article, the technique has been modified and...
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