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theQmechanic
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Homework Statement
A charged particle (q), mass (m) is released from a frictionless inclined plane of angle θ under influence of Earth's acceleration (g) and magnetic field (B) perpendicular to (g) and plane of motion of particle. The particle slides down distance "l" along incline and then follows a cycloidal path with vertical displacement between highest and lowest point (h). Prove that [itex]l = h\frac{cot^{2}θ}{4}[/itex]
Homework Equations
F= qv[itex]\times[/itex]B
The Attempt at a Solution
In vector notation I took g as -g j. B as -B k.
Took instantaneous velocity as v= vxi + vy j.
Then formed a differential equation to vx and vy in terms of time. The point where it leaves the incline is the point of inflection of the curve. I bashed whatever equations I had to finally get the answer, but after doing this I think there's got to be an easy way to look at this. Can someone help me out?