Level 1 - Physics Paper 2

Three point charges are fixed on the \(x\)-axis. A charge \(+3.00\,\mathrm{nC}\) is at \(x=-0.300\,\mathrm{m}\), a charge \(-6.00\,\mathrm{nC}\) is at the origin, and a charge \(+3.00\,\mathrm{nC}\) is at \(x=+0.300\,\mathrm{m}\). Point \(P\) is at \(x=+0.150\,\mathrm{m}\). Take \(V(\infty)=0\).

A safety interlock uses a \(470\,\mu\mathrm{F}\) capacitor initially charged to \(24.0\,\mathrm{V}\). The capacitor discharges through a \(3.30\,\mathrm{k\Omega}\) resistor into a sensor input. When the capacitor voltage falls to \(6.00\,\mathrm{V}\), a separate switch opens an inductor branch that had been carrying \(1.80\,\mathrm{A}\). The inductor has \(L=0.250\,\mathrm{H}\) and then discharges through a \(10.0\,\Omega\) safety resistor.

A proton beam strikes stationary protons in a fixed-target experiment. The proton rest energy is \(m_pc^2=938\,\mathrm{MeV}\). Consider the possible reaction \(p+p\to p+p+X\), where \(X\) is a neutral particle with rest energy \(135\,\mathrm{MeV}\). Use units in which energies are in \(\mathrm{MeV}\) and momenta are in \(\mathrm{MeV}\,c^{-1}\). The relativistic energy-momentum relation is \[ E^2=(pc)^2+(m_pc^2)^2. \] For this fixed-target geometry, the centre-of-mass energy satisfies \[ E_{\mathrm{cm}}^2=2m_p^2c^4+2E m_pc^2, \] where \(E\) is the incident proton's total energy.

A photoelectric detector uses ultraviolet light of wavelength \(240\,\mathrm{nm}\) on a metal photocathode with work function \(2.10\,\mathrm{eV}\). The emitted electrons then enter an electron-diffraction stage, where the fastest electrons are accelerated through an additional \(150\,\mathrm{V}\) before reaching a thin crystal. For photon calculations, take \[ hc=1240\,\mathrm{eV\,nm}. \]