Level 1 - Physics Paper 2

Two square insulating sheets are mounted parallel to one another to make a simple field cage. Each sheet has area \(A=0.120\,\mathrm{m^2}\), and the separation is \(d=3.00\,\mathrm{mm}\). The left sheet has charge \(+Q=8.50\,\mathrm{nC}\) spread uniformly over it, and the right sheet has charge \(-Q\) spread uniformly over it. Treat the sheets as very large compared with their separation, so edge effects may be ignored. The field magnitude from one very large uniformly charged sheet is \[ E=\frac{\sigma}{2\epsilon_0}. \] The field is directed away from a positive sheet and toward a negative sheet.

A beam of singly charged positive ions enters a velocity selector travelling in the \(+\hat{\imath}\) direction. In the selector, \(\vec E=1.80\times10^4\,\hat{\jmath}\,\mathrm{N\,C^{-1}}\) and \(\vec B=0.300\,\hat k\,\mathrm{T}\). Ions that pass undeflected then enter an analyser containing only a uniform magnetic field of magnitude \(0.500\,\mathrm{T}\). Two isotopes have masses \(m_1=3.32\times10^{-26}\,\mathrm{kg}\) and \(m_2=3.49\times10^{-26}\,\mathrm{kg}\).

Two camera flashes occur along a straight train platform. In the platform frame \(S\), flash A occurs at \(x_A=0\), \(t_A=0\), and flash B occurs at \(x_B=600\,\mathrm{m}\), \(t_B=1.00\,\mu\mathrm{s}\). Another inertial frame \(S'\) moves along \(+x\) relative to the platform. For a frame \(S'\) moving at speed \(u\) along \(+x\) relative to \(S\), the Lorentz transformation for separations is \[ \Delta t'=\gamma\left(\Delta t-\frac{u\Delta x}{c^2}\right) \] and \[ \Delta x'=\gamma(\Delta x-u\Delta t). \]

An electron is confined in a one-dimensional infinite square well. The original well width is \(L_0=0.500\,\mathrm{nm}\), but the well is then widened to \(L=0.750\,\mathrm{nm}\). For width \(L\), the stationary-state energies are \[ E_n=\frac{n^2h^2}{8m_eL^2} \] and the normalized wavefunctions are \(\psi_n(x)=\sqrt{2/L}\sin(n\pi x/L)\) for \(0<x<L\).