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Given that the electromagnetic power radiated by a nonrelativistic moving point charge q having acceleration a is:

[tex]P = \frac {q^2a^2}{6 \pi \epsilon_0 c^3} [/tex]

(This formula was presented without discussion or explanation in the problems section of my textbook.)

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 is radiated by this proton?

This looks like one of those dumb problems where you just plug numbers into a formula, but ... what's a in this situation? We are not given the voltage difference between the dees of the cyclotron. So I thought maybe I can use the exit velocity of the proton of the proton given by

[tex]v = \frac {qBr}{m}[/tex]

[tex]a = \frac{v^2}{r} = \frac{q^2B^2r^2}{m^2r}[/tex]

[tex]a^2 = \frac{q^4B^4r^2}{m^4}[/tex]

[tex]P = \frac {q^2a^2}{6 \pi \epsilon_0 c^3} [/tex]

(This formula was presented without discussion or explanation in the problems section of my textbook.)

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 is radiated by this proton?

This looks like one of those dumb problems where you just plug numbers into a formula, but ... what's a in this situation? We are not given the voltage difference between the dees of the cyclotron. So I thought maybe I can use the exit velocity of the proton of the proton given by

[tex]v = \frac {qBr}{m}[/tex]

**Edited:**

OK. It turns out that was the right approach. Only I went off talking about angular acceleration, when I should be dealing with centripetal acceleration. So, the following lines of tex are garbage. The corrected stuff is in the next post.OK. It turns out that was the right approach. Only I went off talking about angular acceleration, when I should be dealing with centripetal acceleration. So, the following lines of tex are garbage. The corrected stuff is in the next post.

[tex]a = \frac{v^2}{r} = \frac{q^2B^2r^2}{m^2r}[/tex]

[tex]a^2 = \frac{q^4B^4r^2}{m^4}[/tex]

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