# Blog

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## 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.

## 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.

## Two-dimensional collisions

This small Python project is a physical simulation of two-dimensional physics. The animation is carried out using Matplotlib's FuncAnimation method and is implemented by the class Simulation. Each "particle" of the simulation is represented by an instance of the Particle class and depicted as a circle with a fixed radius which undergoes elastic collisions with other particles.

## Packing circles inside a shape

A previous blog post dealt with packing circles into a circle. To fill an arbitrary shape, a slightly different approach is needed. The code presented in my github repo.

## Packing circles in a circle

The following code attempts to pack a predefined number of smaller circles (of random radii between two given limits) into a larger one.