Transformation to a r. frame in which E and B are parallel

egutierrezposse
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This is problem 11.15 of Jackson, Classical Electrodynamics

In a certain reference frame a static, uniform, electric field Eo is parallel to the x axis, and a static, uniform, magnetic induction Bo = 2Eo lies in the xy plane, making an angle theta with the axis. Determine the relative velocity of a reference frame in which the electric and magnetic fields are parallel.


I need the resolution for a general Lorentz transformation (not-only in the z-axis)

Thanks
 
Hello, egutierrezposse. Welcome to PF!

According to forum rules, we need to see some attempt at a solution.

Try to convince yourself that a boost in the z direction will do the trick.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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