Module 3 : Electromagnetism
Lecture 13 : Electric Current and Current Density

where $x_0, y_0$and $z_0$are constants of integration representing the initial position of the particle. The equation to the projection of the trajectory in the x-y plane is given by

\begin{displaymath}(x-x_0)^2 + (y-y_0)^2 = \frac{u_x^2}{\omega_c^2}\end{displaymath}

which represents a circle of radius $u_x/\omega_c$, centered about $(x_o, y_0)$. As the z- component of the velocity is constant, the trajectory is a helix.

\includegraphics{helical.eps}

A plot of the motion of a charged particle in a constant magnetic field.

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