Chapter 27, Problem 34P

(II) The path of protons emerging from an accelerator must be bent by 90° by a “bending magnet” so as not to strike a barrier in their path a distance d from their exit hole in the accelerator. Show that the field $\stackrel{\to }{B}$ in the bending magnet, which we assume is uniform and can extend over an area d × d, must have magnitude $B\ge {\left(2mK/e^2{d}^2\right)}^{\frac{1}{2}}$, where m is the mass of a proton and K is its kinetic energy.