How to calculate period in magnetic field?
If we have a charged particle in a magnetic field, then the period of its rotation can be determined using Newton's second law
T=2πR/vT=2\pi R/vT=2πR/v
F=ma→qvBsinα=mv2⋅sin2αRF=ma\to qvB\sin\alpha=m\frac{v^2\cdot \sin^2\alpha}{R}F=ma→qvBsinα=mRv2⋅sin2α →\to→
v=qBRmsinαv=\frac{qBR}{m\sin\alpha}v=msinαqBR
Finally
T=2πRmsinαqBR=2πmsinαqB.T=\frac{2\pi Rm\sin\alpha}{qBR}=\frac{2\pi m\sin\alpha}{qB}.T=qBR2πRmsinα=qB2πmsinα. Answer
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