Volt Track
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cyclotron-where am i going wrong still??
ok so here's the question, followed by what i thought was the way to do the problem. hopefully someone can steer me back on track
An electron moves on a circular orbit in a uniform magnetic field. The strength of the field is 2.50×10-4 tesla. The kinetic energy of the electron is 104.0 eV. (1 eV = 1 electron volt = 1.6 ×10-19 joules.) Calculate the radius of the orbit.
(electron parameters: the charge is -e where e = 1.602×10-19 C; the mass is m = 9.11×10-31 kg.)
ok i solved for velocity by doing K=.5mv^2. Then tried
doing mv^2/r=Bqv (using strength of field for B, electron
charge for q, mass for m, velocity for v) and got
2.42E-16 which apparently is wrong
can anyone help determine where i'm going wrong?
probably don't need to use relativistic speeds and speed of light..because this is like physics 101 course...
is there an easier way?
Don't know where you got that answer. But you should always work problems out symbolically first because these problems are especially prone to calculation errors. Do all calculation only at the end.
Solve for v: KE = kinetic energy = 1/2 mv^2
v = sqrt(2 KE/m)
Then we have the centripetal force being supplied by the magnetic lorentz force:
mv^2/r = qvB
mv/r = qB
r = mv/qB
r = m / qB * sqrt(2 KE / m)
r = 1 / qB * sqrt(2 KE m)
q = 1.6e-19 C
B = 2.5e-4 Tesla
KE = 104eV * 1.6e-19 J/ev = 1.66e-17 J
m= 9.11e-31 kg
When you plug these numbers in, you get r = 0.137 m
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