I solve the differential equation that describes the motion of an oscillating electron that radiates energy. During this analysis, I describe one of the main pitfalls that people run into when using the self force.
I show off some new concept art for future posts.
I am rolling out new icons to help you sort through the difficulty and content of each blog post.
I derive the expression for the Abraham-Lorentz force (i.e. the self-force) and set up the differential equation for the oscillatory motion of a radiating electron near a charged ring.
I calculate the electric field along the axis of a ring of charge. Then, I derive the equation of motion for an oscillating electron about the center of the ring.
I explain how to recover the equations for Newtonian energy and momentum from the low-speed limit of the Lorentz factor.
I derive the relativistic Doppler shift equation in three different ways. The first derivation uses only the definition of time dilation. The second derivation uses a Lorentz boost along the direction of motion. The third derivation uses the general matrix formalism of special relativity.
I visualize the heat kernel and explain how it is used in the diffusion equation.
I go through some of the properties of the simple magnifier (i.e. a magnifying glass) and derive its angular magnification.
I describe how to count the theoretical maximum number of bright spots for a double slit interference experiment.
