The radii of charges moving in a magnetic field

[satxer]

1. A proton and an electron, with the same kinetic energies, enter a magnetic field and both attain circular orbits. What is the ratio of the radii of the orbits to each other?



KE = qvB = (mv^2)/r --> r = mv/qB



3. We know both q values and both m values. The B value is irrelevant. I've tried substituting arbitrary measurements for the velocity and radii of one of the particles, but that still leaves me with two variables to solve for the other particle (v and r). I have no idea what to do now...

 

[berkeman]

1. A proton and an electron, with the same kinetic energies, enter a magnetic field and both attain circular orbits. What is the ratio of the radii of the orbits to each other?



KE = qvB = (mv^2)/r --> r = mv/qB



3. We know both q values and both m values. The B value is irrelevant. I've tried substituting arbitrary measurements for the velocity and radii of one of the particles, but that still leaves me with two variables to solve for the other particle (v and r). I have no idea what to do now...

I don't think your equation is correct. The Lorentz Force gives that the centripetal force is qvB, so it couldn't be the KE. Use KE = 1/2 mv^2 for each particle. Different masses give different velocities. Then use the Lorentz Force...

 

[satxer]

OMG you're right. Thanks so much. How stupid of me. I got the formula (mv^2)/r confused with (mv^2)/2

Please be so kind as to assuage my severely bruised ego with anecdotes of any past careless mistakes you have made

 

[berkeman]

OMG you're right. Thanks so much. How stupid of me. I got the formula (mv^2)/r confused with (mv^2)/2

Please be so kind as to assuage my severely bruised ego with anecdotes of any past careless mistakes you have made

No worries. Lorentz force problems are some of my favorites.