# J.J. Thomson's m/e Experiment, Help!

1. Apr 10, 2012

### SuicideSteve

1. The problem statement, all variables and given/known data

In Thomson's experimental determination of the ratio m/e of the mass to the charge of an electron, in which the electrons were subjected to an electric field of intensity E and a magnetic field of intensity H, the equations

m(d2x/dt2) + He(dy/dt) = Ee , m(d2y/dt2) - He(dx/dt) = 0 ,

were employed. If x=y=dx/dt=dy/dt=0 for t=0, show that the path is a cycloid whose parametric equations are:

x = {Em/H2e}(1 - cos([He/m]t))
y = {Em/H2e}([He/m]t - sin([He/m]t))

3. The attempt at a solution

I have solved the differential equation by substituting 1 for the constants and come out with:
x = 1 - cost
y = t - sint

My problem is I can not figure out how to end up with the constants in the results.

Any help is greatly appreciated,
Thanks.
Steve.

Last edited: Apr 11, 2012
2. Apr 10, 2012

### Ray Vickson

There is something wrong with your two differential equations, since an "E" appears in the stated solution but is not present in your DEs.

RGV

3. Apr 10, 2012

### SuicideSteve

Sorry, fixed it.