Determining Whether Voltage Lags or Leads Current in an RLC Circuit Extra Class Exam Style

If you're coming in from the physics side
In my spare time I write web apps. I also play with ham radios as KD0FNR.  One of the web apps I've published provides practice exams for ham radio license tests.  What follows is a study video for the extra class exam.  The extra class license is the highest class of license an amateur operator can earn in the United States and the test requires quite a bit of electronics theory.

If you're coming in from the ham radio side
For my full time gig, I'm a graduate student in the physics department at Texas A&M University.  In my spare time, I write about physics topics that catch my eye on any given day.

Now for the study video
This study topic details how to work through the questions on the exam that ask about the phase relation between voltage and current in a series RLC circuit.  It shows a few tricks for doing the problems without a calculator.  All feedback is welcome.. please!  As for me, I feel this video is a bit flat, (there aren't any pirates or a moose), but I believe it gets the basic points across.  #E_5_B_07

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…