(4) To save your results for later analysis, write the final particle trajectories for different initial conditions to one or several text files.3 (3) Find a test condition to estimate the accuracy of your numerical solution.2

Use the simple Euler’s method1 to solve the equation of motion in 3 dimensions. Experi- ment with different velocities to get a feeling for the effect of the magnetic field on the particles. protons) coming in with (initially) constant velocity along the x axis. (2) Model the solar wind as charged particles (e.g. Choose the x axis from the Sun toward the Earth and the z axis perpendicular to the ecliptic. Plot the magnetic field in at least 2 of the 3 planes through the origin: the xy and xz planes. (1) Model the Earth as a sphere with a magnetic dipole embedded at its centre (remember that the direction of the magnetic dipole is tilted with regard to the ecliptic). When she asks you how these charged particles actually move around, you are embarrassed: you have no idea! However, you quickly come up with a plan: You wave your hands and tell her about charged particles. Your mother asks you what the aurora is-after all, you should know, being a physicist. Suddenly, you are awed by the appearance of a beautiful display of aurora borealis above your heads.

You are out walking at night with your mother during your christmas holiday. My work on the midterm assignment in TFY4240 Electromagnetic theory at NTNU autumn 2013. TFY4240 Electromagnetic theory - Midterm assignment

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