Many hospitals use a cyclotron to produce radioactive isotopes for nuclear imaging or nuclear medicine. A cyclotron uses a strong magnetic field to keep protons moving in circular orbits. A proton begins in a small diameter orbit with a low speed, but it is gradually accelerated—with a clever use of electric fields—to higher and higher speeds. This causes the orbit’s diameter to gradually increase until the proton exits the machine from a large-diameter orbit. One commercial cyclotron uses a 2.0 T magnetic field. The proton’s acceleration is equivalent to moving through a potential difference ∆V = −1000 V per orbit. How long does it take a proton to move out from its initial orbit to its final orbit?
