- #1
JHans
- 36
- 0
The electromagnetic power radiated by a nonrelativistic particle with charge q moving with acceleration a is:
[tex]
P = \frac{q^2 a^2}{6 \pi \epsilon_0 c^3}
[/tex]
If a proton is placed in a cyclotron with a radius of 0.500 m and a magnetic field of magnitude 0.350 T, what electromagnetic power does this proton radiate just before leaving the cyclotron?
I've identified that the unknown variable for the electromagnetic power equation is the acceleration of the particle, a. To find this, I've identified that the velocity of a particle in a cyclotron is:
[tex]
v = \frac{q B r}{m}
[/tex]
It makes sense to me that by differentiating,
[tex]
a = \frac{dv}{dt}
[/tex]
[tex]
\frac{dv}{dt} = \frac{qB}{m} \frac{dr}{dt}
[/tex]
The problem is that I don't know what the rate of change of the cyclotron's radius (with respect to time) is. Am I going in the right direction, or am I making things more difficult than they need to be?
[tex]
P = \frac{q^2 a^2}{6 \pi \epsilon_0 c^3}
[/tex]
If a proton is placed in a cyclotron with a radius of 0.500 m and a magnetic field of magnitude 0.350 T, what electromagnetic power does this proton radiate just before leaving the cyclotron?
I've identified that the unknown variable for the electromagnetic power equation is the acceleration of the particle, a. To find this, I've identified that the velocity of a particle in a cyclotron is:
[tex]
v = \frac{q B r}{m}
[/tex]
It makes sense to me that by differentiating,
[tex]
a = \frac{dv}{dt}
[/tex]
[tex]
\frac{dv}{dt} = \frac{qB}{m} \frac{dr}{dt}
[/tex]
The problem is that I don't know what the rate of change of the cyclotron's radius (with respect to time) is. Am I going in the right direction, or am I making things more difficult than they need to be?