(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle of charge q starts from rest at the origin of coordinates in a region where there is a uniform electric field of strenthEparallel to the x-axis, and a uniform magnetic fieldBparallel to the z-axis.

Find the equations of motion, and solve them to show that the coordinates of the particle at a time t later will be:

x = (E/B*omega)*(1 - cos(omega*t))

y = - (E/B*omega)*(omega*t - sin(omega*t))

z = 0

where omega = q*B/m. (The path of the circle is a cycloid.)

2. Relevant equations

The parametric equation of a cycloid:

x = constant*(1 - cos(omega*t))

y = constant*(omega*t - sin(omega*t))

The force acting on the particle:

F = q*E+ q*vxB

3. The attempt at a solution

I've done some work on this problem and so far the equations of motion that I've got for the particle are as follows:

1) F(x) = q*E + q*v(y)*B -> x[double-dot] = q*E/m + omega*y[dot]

2) F(y) = -q*v(x)*B -> y[double-dot] = -q*B*x[dot]

I've tried integrating these equations once (eg. integrate 2)) and then substituting this into the other equation. This then gave me:

x[double-dot] + omega^2*x = E*B

And this is where I'm stuck. This has the form of a simple harmonic oscillator, except that the r.h.s. isn't zero, so I can't solve it. Also, I'm not even sure if everything that I've done so far is correct.

Any help on this would be very much appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Electromagnetism - Lorentz Force

**Physics Forums | Science Articles, Homework Help, Discussion**