This java applet show charged particle motion in uniform magnetic field.(2D case)
When the charged particle is within a magnetic field, the radius of the circular motion is quite small and the frequency is huge.
The frequency do not depend on the energy of the particle.
Particle with mass m, charge in a uniformed magnetic field Bz.
If the velocity is perpendicular to the field (Vx,Vy)
The magnetic force F = q (VXB) where Fx= q Vy Bz, Fy= -q Vx Bz , Fz=0.
From Newton's law F = m a, where a has three components ax,ay,az
ax= w*Vy, ay=-w*Vx, az=0.
d2/dx2(Vx)=d/dx(ax)=d/dx(w*Vy)=w*d/dx(Vy)=w*ay = -w2*Vx d2/dx2(Vy)=d/dx(ay)=d/dx(-w*Vx)=-w*d/dx(Vx)=-w* ax = -w2*Vy
w=qBz/m is the angular frequency of the circular motion.
The big gray area represent the uniform magnetic field. (perpendicular to the screen)
Three blue little circles are charged particles.
Click with LEFT mouse button to drag the particle with the animation area.
Click with RIGHT button to change its velocity.(red segment)
Selected particle will be shown in green.
If click mouse button twice, some buttons will show up for you to modify mass or charge.
Click the button, use mouse to drag the slide bar
Click the lightGray area before the number to toggle the sign.
Right/Left click the yellow region to multiply/divide the number by 10.
Click other area twice will switch off modification mode.
Right click mouse button will toggle animation.
Left click mouse button will step forward a small amount of time.
Left click mouse twice will clear the trajectory and reset time.
Blue circles are charged particles. Left Click and drag it inside the magnetic field(lightgray circle)
Right click particle and drag the mouse to change its velocity.
Right Click other locations will toggle the animation.
If particle move outside the boundary, a new particle will be created at the same initial position.
Try all possible cases:e.g. watch how particle across boundary!