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Q)

what will the motion of a charged particle in a cyclotron if the frequency of the radio frequency field is doubled ?

$\begin{array}{1 1} \text{the radius of the path in the dees of the changed particle is also doubled} \\ \text{the radius of the oath in the dees of the changed particle is halved} \\ \text{the radius of the path in the dees of the changed particle is reduced by 2 times}\\ \text{the radius of the oath in the dees of the changed particle is unchanged}\end{array} $

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A)
Solution :
Time period of revolution of changed particle in cyclotron $T= \large\frac{2 \pi m}{Bq}$
$\gamma = \large\frac{1}{T} =\frac{Bq}{2 \pi m}$
If $ \gamma'= 2\gamma$
then $T^1= \large\frac{1}{\gamma^1}=\frac{1}{2 \gamma}$
$\quad= \large\frac{1}{2} \times \frac{2 \pi m}{Bq} $
$\quad= \large\frac{ \pi m}{Bq}$
$\quad= a \;constant$
This clearly states that the charged particle will accelerate and decelerate alternately between the dees of cyclotron .
Answer :the radius of the oath in the dees of the changed particle is unchanged
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