1.

Show that in a cyclotron inside the dee, the time taken to complete half circular path is not dependent on the radius of the path.

Answer»

For cyclotron
\(\frac{m v^{2}}{r}\) = qvB
Here m is mass of charge particle, v is velocity of particle, Bis magnetic field.
∴ Radius of the path
r = \(\frac{m v}{q B}\)
Periodic time, T = \(\frac{2 \pi r}{v}=\frac{2 \pi m}{q B}\)
∴ Time spent in semicircle
\(\frac{T}{2}=\frac{\pi m}{q B}\)


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