# Blog

A blog of Python-related topics and code.

## Visualizing the Earth's dipolar magnetic field

The magnetic field due to a magnetic dipole moment, $\boldsymbol{m}$ at a point $\boldsymbol{r}$ relative to it may be written $$\boldsymbol{B}(\boldsymbol{r}) = \frac{\mu_0}{4\pi r^3}[3\boldsymbol{\hat{r}(\boldsymbol{\hat{r}} \cdot \boldsymbol{m}) - \boldsymbol{m}}],$$ where $\mu_0$ is the vacuum permeability. In geomagnetism, it is usual to write the radial and angular components of $\boldsymbol{B}$ as: \begin{align*} B_r & = -2B_0\left(\frac{R_\mathrm{E}}{r}\right)^3\cos\theta, \\ B_\theta & = -B_0\left(\frac{R_\mathrm{E}}{r}\right)^3\sin\theta, \\ B_\phi &= 0, \end{align*} where $\theta$ is polar (colatitude) angle (relative to the magnetic North pole), $\phi$ is the azimuthal angle (longitude), and $R_\mathrm{E}$ is the Earth's radius, about 6370 km. See below for a derivation of these formulae.

## Some analysis of the demographics of India

This Jupyter Notebook can be downloaded and viewed at my GitHub repository.

## Impact craters on Earth

The Earth Impact Database is a collection of images, publications and abstracts that provides information about confirmed impact structures for the scientific community. It is hosted at the Planetary and Space Science Centre (PASSC) of the University of New Brunswick.

## The Star Wars opening crawl in Matplotlib

Matplotlib isn't the obvious choice for depicting the Star Wars opening crawl, but that isn't a reason not to try:

## A simple two-dimensional Brownian motion animation

This code continues the previous blog post on two-dimensional collisions to model Brownian motion. The code is on my GitHub page.