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

1.

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

2.
Choose the z-axis to lie in direction of B and let the plane containing E and B be the yz-plane.
Thus:
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

3.
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

4.
Integrate the velocity equation from (3) and show (with appropriate initial conditions - see attached file) that:

... radius is that of particle 3), its mass can't be the greatest. This solution helps answer question regarding particles injected in a uniform magnetic field. ...

Motion of a charge particle in a magnetic field. 1) What is the initial direction of deflection for the charged particles entering the magnetic fields as shown ...

... a speed of 1.85 x 10^7 m/s. How large a magnetic field is required to bend the path of the particles into a circle of 0.580-m radius? An alpha particle has a ...

... is projected vertically upward with a speed of 2.30 106 m/s into a uniform magnetic field of 0.190 T ... Solution: Magnetic force on a moving charged particle is. ...

... force equation ---- (1) ie F = qvB sin, where is the angle between the direction of the velocity of the charged particle moving in magnetic field. ...

... charged particle in uniform electric and magnetic fields that are ... Eey and a perpendicular uniform magnetic field B = Bez ... equations of motion for the particle...

... shows 11 paths through a region of uniform magnetic field. ... charges and speeds of the 11 particles that take ... Which path corresponds to which particle in the ...

...magnetic forces acting on charged or uncharged particles? ...magnetic force that a charged particle can feel is when it is moving parallel to the magnetic field. ...