The magnetic field is always in the y direction, However, you can enter Ex,Ey,Ez to add electric field to the system.
The force for charge particle in the electric and magnetic field is
If the initial velocity is proportional to the magnetic field and there is no electric field presented, then the force is always perpendicular to the velocity and magnetic fiel d, which means that it is a circular motion , so , or which is a independent on the velocity of the particle. it only depends on and magnetic field B.
This java applet tries to show :
The motion of a charged particle in a uniform and constant electric/magnetic field
- 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 the textfield.
- 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)
Press start button to start the animation
- 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 plane.
- 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 to resume.
- 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 initial condition
- If the trace is saved, you can view the trace from various angle.
- Press Reset button to reset the condition
You might want to check out [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1431.0]EJS version of Charged particle motion in E/B Field[/url]
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
- 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 magnetostatic field.