How Do Proton and Electron Path Radii Compare in a Magnetic Field?

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In a magnetic field, the ratio of the radii of circular paths for a proton and an electron with the same kinetic energy can be derived from their respective masses and velocities. The gyroradius is directly proportional to the momentum of the particle, and the forces acting on the particles include the magnetic force and the centripetal force. The relationship between the radii can be expressed as r(e) : r(p) = - (m(e)v^2)/BV : (m(p)v^2)/BV, where m represents mass, v is velocity, and B is the magnetic field strength. The discussion emphasizes the need to consider the Lorentz force and the principles of circular motion to accurately calculate the path radii. Understanding these relationships is crucial for solving problems related to charged particles in magnetic fields.
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This Is A Challenging One...

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

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
 
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.
 
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