particle motion in E/M Field
This java applet tries to show :
Press start button to start the animation
The motion of a charged particle in a uniform and constant electric/
- Particle starts at the origin of the coordinate system
- Blue arrow starts from the origin shows
the magnetic field (always in the Y direction)
- Red arrow starts
from the origin shows the electric field.
- LEFT Click near the tip of the
arrow, and drag the mouse to change the E field (Both direction and magnitude),
The black arrow on X-Z plane shows the drift velocity Vd
- You can also key in values in the textFields to change E / B fields.
- Do not forget to hit the RETURN key after enter the value into
- Change the coordinate system:
- Translation : LEFT Click near the
origin, and drag the mouse
- Rotation: RIGHT Click within the window
and drag the mouse
- Change the initial Velocity V:
- Left click the mouse button within the window and drag the mouse
- The above changes depend on where you press the mouse button.
- (X-Y, Y-Z or Z-X plane, watch the color of the axis)
- The position, initial velocity and the period of the motion are shown
at the top left region.
- During the animation
- If the trajectory is not on the X-Z plane :
- Its color is GREEN
- The black curve shows projection of the trajectory on the X-Z
- RED arrow reprenents velocity of the charge
- BLUE arrow represents the force acting
on the charge.
- Press the LEFT mouse button will suspend the animation, press it again
- Click the checkbox on the right to save
all the traces
- Drag the RIGHT mouse button to change the viewing angle.
- Animation resumes when you release the mouse button -- with the same
- If the trace is saved, you can view the trace from various angle.
- Press Reset button to reset the condition
The Lorentz frce acting on a point charge q is given by
F = m a = q ( E + V X B )
- If E=0. ˇGF = q V X B is perpendicular
to both V and B (example 1)
- If initial velocity V is perpendicular to magnetic field B,
the change will move in a circular orbit with
- P = m V = q R X B
- (R is the radius of the circular motion)
- The period of the motion is not depend on the velocity
- the angular frequency (also known as cyclotron frequency)
- w = q B / m
- Try with larger q/m value (let q/m=0.1) ! charge moves along B field
- If EXB exists, the charge will drift in that direction with
drift velocity Vdrift = EXB/|B|2
- called "E cross B drift " (example
2) ( example 3)
- Try it with a larger q/m value ( let q/m=0.1 => smaller radius R)!
- The work done by the field will increase the kinetci energy of the
change particle K = q EˇER (R is the displacement vectorˇ^
- Particles with different velocities will spread out in E field
- Magnetostatic field can not change the kinetic energy of the particle
( only change the direction of its velocity, F is always perpendicular
to its velocity Vˇ^
- The cyclotron frequency does not depend on the speed of the particle
or the radius of the orbit.
- Particles with different velocities will not spread out in a uniform
Your suggestions are highly appreciated! Please click firstname.lastname@example.org
AuthorˇGFu-Kwun Hwang, ( click me for more physics related java applet )
Dept. of physics, National Taiwan Normal University
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