Question Number 53156 by peter frank last updated on 18/Jan/19
Answered by peter frank last updated on 18/Jan/19
$${eV}=\frac{\mathrm{1}}{\mathrm{2}}{mv}^{\mathrm{2}} \\ $$$$\frac{{e}}{{m}}=\frac{{v}^{\mathrm{2}} }{\mathrm{2}{V}} \\ $$$$ \\ $$
Answered by peter frank last updated on 18/Jan/19
$${ii}\:\:\:\:\:{eV}=\frac{\mathrm{1}}{\mathrm{2}}{mv}^{\mathrm{2}} ......\:\left({i}\right) \\ $$$${v}=\frac{{E}}{{B}}............\left({ii}\right)\left[{F}_{{e}\:} ={F}_{{m}\:} ={eE}={Bev}\right. \\ $$$${sub}\:{eqn}\:{ii}\:{in}\:{i} \\ $$$$\frac{{e}}{{m}}=\frac{{E}^{\mathrm{2}} }{\mathrm{2}{VB}^{\mathrm{2}} } \\ $$$${E}=\frac{{v}}{{d}} \\ $$$$\frac{{e}}{{m}}=\frac{{E}^{\mathrm{2}} }{\mathrm{2}{VB}^{\mathrm{2}} } \\ $$$${k}=\frac{{v}}{{B}^{\mathrm{2}} } \\ $$$${kB}^{\mathrm{2}} ={v} \\ $$$${B}^{\mathrm{2}} \alpha\:{v} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$