Question
Verify that the cyclotron frequency $ω = eB/m$ has the correct dimensions of $[T]^{–1}.$
✓
Answer
For a charge particle moving perpendicular to the magnetic field:
$\frac{(\text{mv}^2)}{\text{R}}=\text{qvB}$
$\Rightarrow\ \frac{\text{qB}}{\text{m}}=\frac{\text{v}}{\text{R}}=\omega$
$\Rightarrow\ =\omega=\frac{\text{qB}}{\text{m}}=\frac{\text{v}}{\text{R}}=[\text{T}]^{-1}$
$\frac{(\text{mv}^2)}{\text{R}}=\text{qvB}$
$\Rightarrow\ \frac{\text{qB}}{\text{m}}=\frac{\text{v}}{\text{R}}=\omega$
$\Rightarrow\ =\omega=\frac{\text{qB}}{\text{m}}=\frac{\text{v}}{\text{R}}=[\text{T}]^{-1}$
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