Several problems are encountered in trying to scale up cyclotrons to produce increasingly energetic protons. One of them is that the external magnets have to be made larger and larger, which is prohibitively expensive and ultimately becomes completely unfeasible. A newer generation of machines called synchrotrons were therefore invented in which protons can circulate at constant radius, so the magnets only need to cover a much smaller area.

(a) In that case, how can relativistic protons be accelerated to higher and higher speeds if their orbital radius remains constant?

(b) The Large Hadron Collider (LHC) of CERN (Organisation Européenne pour la Recherche Nucléair) accelerates protons up to total energies as large as \(7.0 \mathrm{TeV}\left(1 \mathrm{TeV}=10^{3} \mathrm{GeV}=10^{6} \mathrm{MeV}\right)\) or perhaps even larger. The circumference of the proton path is \(27 \mathrm{~km}\), lying in an underground tunnel near Geneva, partly in Switzerland and partly in France. What magnetic field \(B\) is required in this case?