# J.J Thomson's determination of of the ratio m/e

1. May 9, 2010

### nddewaters

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) , 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))

Good Luck.

2. May 22, 2010

### IPhO' 2008

find $$\Sigma$$Fx $$\Sigma$$Fy in terms of E,H,e etc.
$$\Sigma$$Fx = md2x/dt2
$$\Sigma$$Fy = md2y/dt2
and solve the differential equations.