Question

Calculate the potential difference needed to accelerate sulfur 32 ions with a charge magnitude of3.2x10^-19 C and mass of 5.35x10^-26kg into a mass spectrometer , with a uniform 3.7-T magnetic field.The radius of the curved path is 1.15cm Calculate the potential difference needed to accelerate sulfur 32 ions with a charge magnitude of3.2x10^-19 C and mass of 5.35x10^-26kg into a mass spectrometer , with a uniform 3.7-T magnetic field.The radius of the curved path is 1.15cm @Physics

Answer 1

In the magnetic field, the magnetic (Lorentz) force will be centripetal. Here, we will assume the magnetic field and the velocity of the particle are perpendicular. \[\frac{mv^2}{r} = qvB\Rightarrow v= \frac{qrB}{m}\]Now, the work done by the field (and thus potential difference U necessary) will be the final kinetic energy K of the particle assuming it is accelerated from rest.
\[U=K=\frac{1}{2}m\left(\frac{qrB}{m}\right)^2=\boxed{\displaystyle \frac{(qrB)^2}{2m}}\]Plug in given values to evaluate the required energy.