Discussion
A charged particle is released from rest in a region where both uniform constant electric field and uniform constant magnetic field are present. If these fields are perpendicular to each other, then the trajectory of the particle is a ........ .
Answer: C
The trajectory is a cycloid.
The electric field starts the particle moving from rest, and the magnetic force \(q\bar{v} \times \bar{B}\) then bends its path. The motion is the sum of a uniform drift with velocity \(\bar{v}_{d} = \frac{\bar{E} \times \bar{B}}{B^{2}}\) and a circular motion at the cyclotron frequency. Because the particle starts at rest, the circular speed equals the drift speed, so the path is that of a point on the rim of a rolling wheel: a cycloid, which momentarily stops at each cusp.
A straight line would need no magnetic force, a circle would need no electric field, and a helix needs an initial velocity component along B.
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