Relativistic trajectory in a constant null crossed field

Choose

B = B e_{z}, E = c B e_{x}, Ω = \frac{qB}{m} .

A particle released from rest at the origin has the proper-time trajectory

t (τ) = τ + \frac{Ω ^{2} τ ^{3}}{6}, x (τ) = \frac{c Ω τ ^{2}}{2}, y (τ) = - \frac{c Ω ^{2} τ ^{3}}{6}, z (τ) = 0.

 Ancestors (6)