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

[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.

 

[IPhO' 2008]

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