A charged particle of charge $\mathrm{e}$ and mass $\mathrm{m}$ is moving in an electric field ${{\rm{\vec E}}}$ and magnetic field ${{\rm{\vec B}}}$ Construct dimensionless quantities and quantities of dimension [T]-1
A charged particle of charge $\mathrm{e}$ and mass $\mathrm{m}$ is moving in an electric field ${{\rm{\vec E}}}$ and magnetic field ${{\rm{\vec B}}}$ Construct dimensionless quantities and quantities of dimension [T]-1
When electron enter in perpendicular magnetic field than magnetic force balance with centripetal force,
$\frac{m v^{2}}{\mathrm{R}}=q v \mathrm{~B}$
$\therefore\frac{q \mathrm{~B}}{m}=\frac{v}{\mathrm{R}}=\omega$
$\therefore\omega=\frac{v}{\mathrm{R}}=\frac{\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}}{\mathrm{~L}^{1}}=\mathrm{T}^{-1}$
Thus, angular frequency having dimension equal to $\mathrm{T}^{-1}$.
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