Series
Electromagnetism I Studied
21 posts
- #1
Electrostatics
Kicking off electromagnetism with electrostatics — what static electricity actually *is*, why charges sit still, and diving straight into Coulomb's law!
· 5 min read - #2
Gauss's Law
A super easy breakdown of Gauss's law using a soy-sauce-flinging analogy — because electric field lines and flux really don't have to be scary, okay?!
· 8 min read - #3
Electric Potential
We dig into electric potential — why curl = 0 lets you define a scalar potential, how E = -∇V falls out of that, and a sneak peek at Poisson's equation~
· 2 min read - #4
Electric Potential (Part 2)
We drag charges into empty space one by one, tally up all the work it takes, and land on a slick double-sum formula for total potential energy!
· 2 min read - #5
Electrostatics in Conductors
A casual walkthrough of why E = 0 inside ideal conductors, how charges spread to the outer surface, and how to handle a nested conductor sphere problem!
· 4 min read - #6
Laplace's Equation
Chapter 3 kicks off with Poisson's and Laplace's equations — what you get when you plug ∇V into Gauss's law and let the charge density go to zero.
· 7 min read - #7
The Method of Images
A breezy walkthrough of the image method — a clever trick for finding the electric potential above a grounded conducting plane by sneaking in imaginary charges.
· 5 min read - #8
Separation of Variables
Assuming V(x,y) = X(x)·Y(y) and hoping for the best — here's how separation of variables lets us crack Laplace's equation step by step!
· 5 min read - #9
Multipole Expansion
Ever wondered what a bunch of charges look like from suuuper far away? Turns out you can approximate the whole mess as a monopole, dipole, quadrupole, and beyond!
· 6 min read - #10
Polarization
Diving into how atoms and dielectrics respond to electric fields — getting polarized, forming tiny dipole moments, and what that α actually means!
· 4 min read - #11
Bound Charge Density
Working through why σ_b = P·n̂ and ρ_b = −∇·P actually make sense, using a hands-on geometric argument about sliced-up polarized volumes.
· 2 min read - #12
Electric Displacement
We define the electric displacement vector D to neatly separate the total electric field from polarization effects inside a dielectric — turns out it plays really nicely with Gauss's law!
· 3 min read - #13
Linear Dielectrics
We dig into linear dielectrics, untangling how polarization P, electric susceptibility χₑ, permittivity ε, and the displacement field D all connect!
· 4 min read - #14
Linear Dielectrics (Part 2)
Why even bother stuffing a dielectric in a capacitor? Turns out it bumps up the capacitance — and Venom-Spider-Man definitely has the cushier gig because of it!
· 5 min read - #15
Lorentz Force and Magnetostatics
Charges gotta move to make magnetism, and the total force they feel from electric and magnetic fields together? That's the Lorentz force!
· 8 min read - #16
The Biot-Savart Law
We 'discovered' the Biot-Savart law — the equation that tells us exactly how big a magnetic field gets around a current-carrying wire, then worked through some examples hehe~
· 3 min read - #17
Ampère's Law
If electrostatics has Gauss's law then magnetostatics has Ampère's law — the line integral of B around any closed loop just equals μ₀i_in, hehe!
· 3 min read - #18
Ampère's Law (Part 2)
Let's actually work through Ampère's law problems — infinite wires, surface currents, and why symmetry is the magic keyword that makes everything ridiculously easy!
· 3 min read - #19
Magnetic Vector Potential
A pinwheel-and-wind intuition-building session on why B=∇×A actually makes sense, explained in the most chaotic-but-fun way possible.
· 4 min read - #20
Magnetic Fields in Matter
Chapter 6 is basically Chapter 4 all over again — once you survived polarization density, the magnetic dipole moment stuff practically explains itself!
· 7 min read - #21
The Auxiliary Field H
Just like D handles free charges in electrostatics, H is the magnetic field due to free currents — saving us from infinite microscopic madness!
· 4 min read