Double Integrals and Magnetic Fields

Just an update on my current self-ed progress!

I struggled this whole week to make the appropriate time to study as much as I wanted.  But the weekend is here and I’ve got my coffee, rest, and time……!

Since the last update I’ve completed two Calculus lectures and one chapter of Physics II (~two lectures).

In calculus I learned about Iterated/Double Integrals for both Cartesian and Polar coordinate systems.  The cool thing about these Integrals is that they are an empirical way to calculate the volumes under curved surfaces.  Like single-variable Integrals used to calculate the area under a curve, such as the parabolic arch under an old-fashioned bridge, these can be used to calculate the Volume under a curved surface—such as under a paraboloid, which rather resembles a Nespresso bullet… [see below]

2015-10-17 11.54.14

This brings me to a point about Multivariable Calculus that I had meant to write about earlier: that most of the topics I’m coming across in MV-Calc are just translations and generalizations of single variable calculus equations and concepts into the 3D coordinate plane.  Most of these also include generalizations for a potentially infinite amount of dimensions, n dimensions.  But as the professor stated in the first MIT Online CourseWare (OCW) Lecture for 18.02, many of the applications for basic MV calc will be for 3 dimensions (x, y, z) because it is difficult to comprehend 4+ dimensions graphically.  We can write them out in formula, but drawing them becomes an issue. [which I will discuss later! because imagining 4D is one of my favorite physical mysteries].

In 8.02 – Physics 2 – Electromagnetism, I’ve finally busted into Magnetism–a topic that will prove most fundamental to my understanding of the containment of deuterium plasma one day, if I choose to go the Tokamak route!

The first 5 chapters of Physics for S&E were focused on basic Electric Fields and Electricity.  Now the next few are on Magnetic Fields before going into more advanced Electromagnetism and the EM-spectrum.  I find the interaction of the Electric and Magnetic fields on charged particles entirely fascinating.  The fact that E-fields and B-(magnetic)-fields can affect the velocity of charged particles in a very precise, calculable manner is exciting because of the potential (and realized) applications.  I think of E- and B- fields as scientists’ hands-at-a-distance that allow us to touch, move, and manipulate the tiny particles.  Awesome!

So my wife has already told me that she won’t allow me to build a nuclear reactor in the house.  But perhaps I can convince her to let me build a particle accelerator.

Physics II Notes Timelapse