Charged Particle in Constant Electromagnetic Field, Lorentz

The motion of a charged particle in an electromagnetic field can be obtained by 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 a charge q and has a velocity v is given by:

F= qE + qv (cross product) B

Where we assume v<< c (the speed of light)

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

r = (mv)/(qB)

b.) Choose thr z axis to lie in the direction of B and let the plane containing E and B be the xy plane.

Then: B = Bk, E= Ey j + Ez k

Show that z(t) = zo = zo't + (qEz)/(2m) t2

Where z(0) = zo and z'(0) = zo'

c.) Continue the calculation and find x'(t) and y'(t); show that the time averages of these velocities are:
(x') = Ey/B, (y') = 0

d.) Integrate the velocitiy equations above (c) with the initial conditions:

... on a particle of mass m that carries charge q and ... the z-axis will be that of constant speed ... this direction (as the question indicates), the particle is confined ...

... The electric field is produced by a second infinite ... first plate, maintained at a constant positive voltage ... consider the motion of a charged particle in uniform ...

...Lorentz force experienced by the charged particle is given by: ... Hence,. Fx = m dvx/dt = 0 (where m = mass of the particle). => vx = constant = v0 (As there is ...

... it is quite diﬀerent from elementary particles such as ... of elementary excitations of the vibration of the particle. ... Exercise 1.6 For a single charge q at ...

... Bohr magneton μB If each lump of charge has mass m ... factor We now know that any particle can have ...Particles and Spin Stern Gerlach Experiment & Hydrogen ...

... j + 15.0k) km/s and a constant acceleration of ... velocity vectors and that due to electric field is along ... The force on a moving charged particle in presence of E ...

... A sin ( Ω B t + φ 0 ) Negatively charged particles (in particular ... consequence of the motion of the charge is that ... r′ The relativistic β of the particle is. ...

... speed V parallel to and at a constant distance d ... the point charge due to the electric current ... As the electrons are negatively charged particles the direction of ...