Walker, Halliday & Resnick — Magnetic Fields: Problem 59

59 A mass spectrometer (Fig. 28-12) is used to separate uranium ions of mass $3.92 \times 10^{-25} \text{ kg}$ and charge $3.20 \times 10^{-19} \text{ C}$ from related species. The ions are accelerated through a potential difference of $180 \text{ kV}$ and then pass into a uniform magnetic field, where they are bent in a path of radius $1.00 \text{ m}$. After traveling through $180^\circ$ and passing through a slit of width $1.00 \text{ mm}$ and height $1.00 \text{ cm}$, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out $100 \text{ mg}$ of material per hour, calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in $1.00 \text{ h}$.