This Is A Challenging One....

[Jack16]

A proton and an electron have the same kinetic energyuopn entering a region of constant magnetic field
What is the ratio of the radii of their circular paths?

I used MeVe squared= MpVp squared
but i couldn't get the ratios from these....

[Tide]

You need to use the fact that the gyroradius varies directly with the momentum of the particle.

[Gonzolo]

Force due to magnetic field : F = qvB, with v perpendicular to F
Force due to circular motion : F = ??? (the most elementary form...)

Mix all of this together using Newton's 3rd.

[davehatton01]

use the fact that in circular motion, F=(mv^2)/r.

after a bit of fiddling that gives you the ratios of the circles:

r(p) = radius for proton path
r(e) = radius of electron path
m(e) = mass of electron
m(p) = mass of proton
v = velocity of particle
B = mag field strength
V = Voltage across plates

r(e) : r(p) = - (m(e)v^2)/BV : (m(p)v^2)/BV

[aekanshchumber]

You are heading wrong way, to calculate take lorentz force in account and try it again
use relation,
(mv^2)/2 = qvb
m mass
v velocity
q charge
b magnetic field.