- #1

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**= q

**v**[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**= v

_{x}

**i**+ v

_{y}

**j**.

Then formed a differential equation to v

_{x}and v

_{y}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?