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Module 3 : Electromagnetism

Lecture 13 : Electric Current and Current Density

The equation to the trajectory is

$\begin{displaymath}\left(x - \frac{E}{B\omega_c}\right)^2 + \left(y - \frac{Et}{B}\right)^2 = \frac{E^2}{B^2\omega_c^2}\end{displaymath}$

which represents a circle of radius

$\begin{displaymath}R = \frac{E}{B\omega_c}\end{displaymath}$

whose centre travels along the negative y direction with a constant speed

$\begin{displaymath}v_0 = \frac{E}{B}\end{displaymath}$

The trajectory resembles that of a point on the circumference of a wheel of radius , rolling down the y-axis without slipping with a speed . The trajectory is known as a cycloid.