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"A particle, X with mass m and charge q starts with an inital velocity zero, and follows the red path indicated on the drawing. It follows a half circle when entering the magnetic field.

A new particle, Y with mass m(same) and charge 2q starts from the same place as X. Is the following true og untrue:

1. The force on Y is double the force on X in the electric field.

2. The force on Y is double the force on X in the magnetic field.

3. The time Y uses on the half circle is half the time X uses.

1. Fex=qE and Fey=2qE. So that's true.

2. Fmx=qvB = q*sqrt(qU/m) * B.

And Fmy = qvb = 2q * sqrt(2qU/m) * B. So this statement is false.

3. I don't get this.

It's half a circle, so v=Pi*r/T

And I have tried the formula: v^2/r = 4Pi^2*r / T^2

But everything I use involves either v, or r og both. And the radius of Y has to be smaller right? Since the mag. force on Y is the biggest. But I don't know the radius! And the speed is such an ugly expression, and I always end up with the square root of an expression, so the difference can't be 1/2.

The book says that statement 3 is true...

Please help.

Thanks

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# Homework Help: Two particles in a magnetic field

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