I have been unable to find a satisfactory explanation of this problem, elsewhere.(adsbygoogle = window.adsbygoogle || []).push({});

Consider an uniform electric field, E, along the y axis. Consider also a uniform magnetic field, B, along the z axis. If we release a particle (charge=q, mass=m) at rest on the origin at time t=0, what will be its dynamics in the case that E>B (in cgs units)?

The manner in which my classmates and I solved the problem was to consider a reference frame boosted along the x axis by speed v=cB/E. Looking at how this transforms the fields, we see that the magnetic field goes to zero, and so in the moving frame, the particle accelerates along the y axis due to the electric field,only. Transforming back to the LAB frame, we see that the particle motion remainssolelyin the y direction.

This seems to be in violation of the Lorentz force equation, which dictates that a charged particle moving in the y direction in the presence of a magnetic field in the z direction should experience a non-zero force in the x direction (note: this is the scenario in the lab frame, which is where the contradiction seems to exist, not in the boosted frame, which seems self-consistent).

Does anyone understand the resolution of this problem? I am hesitant to conclude that special relativity is wrong.

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# I E cross B field, with E>B

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