Electromagnetism

Measure Internal Resistance of Battery

How to Measure Internal Resistance of a Battery

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Introduction A commonly encountered school-level Physics practical is the determination of the internal resistance of a battery - typically an AA or D…
gauss law misconceptions

A Physics Misconception with Gauss’ Law

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3 Comments
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…
model magnet

How to Model a Magnet Falling Through a Conducting Pipe

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7 Comments
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…
model magnet

How to Model a Magnet Falling Through a Solenoid

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11 Comments
Introduction Modeling a magnet realistically is a task best done numerically.  Even the simplified model of two separated disks with uniform surface…
magnetism current

Symmetry Arguments and the Infinite Wire with a Current

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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…
electromagnetic computations duality

Building a Numerical FEM Solver for Duality in EM Fields

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In the previous insights article (How to Use Duality in Computational Electromagnetic Problems), I covered some uniqueness theorems for the Riemann-Silberstein…
electromagnetic computations

How to Use Duality in Computational Electromagnetic Problems

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1 Comment
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…
Split Electric Fields

Es vs Em Fields in Electrodynamics: Capacitor & Antenna

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Abstract The analysis of the two kinds of electric fields, namely the irrotational and non-conservative, is extended to electrodynamics, as exemplified…
electric potential

Electric Vector Potential: Detect Non-Conservative Fields

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16 Comments
Main Point The electric vector potential offers a means of determining the non-conservative component of a mixed stationary or quasi-stationary electric…
electromagentic waves traverse

Are Electromagnetic Waves Always Transverse? Full Explanation

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5 Comments
In this insight, we will explore classical electrodynamics and examine whether electromagnetic (EM) waves are always transverse. We use Jefimenko's equations…

How to Recognize Split Electric Fields

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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. …
maxwell magneto

Maxwell’s Equations in Magnetostatics and Solving with the Curl Operator

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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…
what is impedance

Impedance in AC Circuits: Definition & Key Equations

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Definition / Summary The impedance of a load (a combination of components) in an AC circuit is a complex number [itex]Z = R + jX[/itex], where [itex]R[/itex]…
Magnetic Field Lines

Are Magnetic Field Lines Real?

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Introduction We recently had a question in the relativity forums that mentioned the behavior of magnetic field lines and reminded me of my confusion at…
walter lewin

Lewin’s Circuit Paradox: Distinguishing E_s and E_m

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65 Comments
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]).…
Maxwell equations

What is the Homopolar Generator: An Analytical Example

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Introduction It is surprising that the homopolar generator, invented in one of Faraday's ingenious experiments in 1831, still seems to create confusion…
magnet

Permanent Magnets Explained by Magnetic Surface Currents

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38 Comments
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…
ohmslaw

Learn Why Ohm’s Law Is Not a Law

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41 Comments
At first, I wanted this title to say “Ohm’s law is not a Law.”  But someone else used that phrase in a recent PF thread, and a storm of protest…
acpoweranalysisp3

Power Grid Cyber Resilience: Risks and Defenses Explained

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9 Comments
Click for Series ListPart 1: The Basics Part 2: Network Analysis Part 3: Cyber ResilienceIntroduction Power system security is much too big…
acpoweranalysisp2

Intro to AC Power Analysis: Network Analysis

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26 Comments
 Let me use the terms “power grid” and “network” interchangeably. What is the Power Grid Required to Do?Deliver energy to customers,…
electrostaticfield1

Learn About Energy Gained by Charge in an Electrostatic Field

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2 Comments
Energy gain of an electron in a potential V I have seen this question being asked frequently on here. A lot of students have a bit of an issue in understanding…
spacetime4

Struggles With the Continuum: Point Particles and the Electromagnetic Field

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 In these posts, we're seeing how our favorite theories of physics deal with the idea that space and time are a continuum, with points described…
lightswitch

What Happens When You Flip the Light Switch: From Zero Seconds to 20 Years

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47 Comments
Introduction Few people know what happens when a customer does something like flipping a light switch. The full explanation requires descriptions of topics…
gausslaw

Derivation of Gauss’s Law: Coulomb to Flux Explained

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3 Comments
Gauss's law was formulated by Carl Friedrich Gauss in 1835. It is one of the four Maxwell's equations that form the basis of classical electrodynamics.…
electrical wire

Mutual Inductance: When k≠1 and Two Coupling Coefficients

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4 Comments
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).…