Purchase Solution

Particle in a magnetic field

Not what you're looking for?

Ask Custom Question

The motion of a charged particle in an electromagnetic field can be obtained from the Lorentz equation for the force on a particle in such a field.
If the electric field vector is E and the magnetic field vector is B the force on a particle of mass m that carries charge q and has velocity v is given by:

F = qE +qv X B


If there is no electric field and the particle enters the magnetic field in a direction perpendicular to the lines of teh magnetic flux, show that the trajectory is a circle with radius

r = mv/qB = v/w

where w=gB/m is the cyclotron frequency

Choose the z-axis to lie in direction of B and let the plane containing E and B be the yz-plane.
B = Bk E = E_y j + E_z k

Show that the z-component of the motion is given by:

z(t) = z(0) + (z_dot(0))*t+(qE_z / 2m) * t^2

Continue the calculation and obtain expressions for dx/dt and dy/dt Show that the time average of these velocity components are:

<dx/dt> = E_y/B <dy/dt> = 0

Integrate the velocity equation from (3) and show (with appropriate initial conditions - see attached file) that:

x(t) = -A/w * cos(wt) + E_y/B *t
y(y) = A/w *sin (wt)

Plot the trajectory for the following cases:

A > E_y/B
A = E_y/B
A < E_y/B

Purchase this Solution

Solution Summary

The solution is 14 pages long including full explanations and derivation of all equations.

Purchase this Solution

Free BrainMass Quizzes
The Moon

Test your knowledge of moon phases and movement.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

Basic Physics

This quiz will test your knowledge about basic Physics.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.