(Solved): viii) Write down the equation of motion for a free particle of charge \( q \) and mass \( m \) movi ...

viii) Write down the equation of motion for a free particle of charge \( q \) and mass \( m \) moving in an electric field \( \underline{E} \) and a magnetic field \( \underline{B} \). Sketch the particle motion when \( \underline{E} \) is perpendicular to \( \underline{B} \) (see figure below) for a charged particle moving from left to right. (ix) Ohm's law for a current induced by a steady electric field in a plasma is given by: \[ \begin{array}{l} \underline{J}=\sigma \underline{E} \\ \text { with } \sigma=\frac{n_{e} e^{2}}{m_{e}} t_{c} \end{array} \] What is the significance of \( \sigma \) and \( \bar{t}_{c} \) You may find the following useful: [2 marks] \[ \begin{array}{l} k_{B}=1.38 \times 10^{-23} \mathrm{JK}^{-1} \\ \mu_{0}=1.26 \times 10^{-6} \mathrm{Hm}^{-1} \\ 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J} \end{array} \]