A cyclotron's oscillator frequency is n and t | vedclass

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(A) The cyclotron frequency is given by $n = \frac{q B}{2 \pi m}$.Rearranging for the magnetic field $B$,we get $B = \frac{2 \pi n m}{q}$.For a proton

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$\frac{2 \pi n m}{q}, \frac{q v B r}{2}$

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(A) The cyclotron frequency is given by $n = \frac{q B}{2 \pi m}$.Rearranging for the magnetic field $B$,we get $B = \frac{2 \pi n m}{q}$.For a proton moving in a circular path of radius $r$ inside the dees,the magnetic force provides the centripetal force: $\frac{m v^2}{r} = q v B$.This simplifies to $m v^2 = q v B r$.The kinetic energy $(K.E.)$ is given by $K.E. = \frac{1}{2} m v^2$.Substituting $m v^2 = q v B r$ into the kinetic energy formula,we get $K.E. = \frac{q v B r}{2}$.

$A$ cyclotron's oscillator frequency is $n$ and the radius of the dees is $r$. The operating magnetic field $(B)$ for accelerating protons of charge $q$ and the kinetic energy of the protons produced by the accelerator are respectively ($m$ and $v$ are the mass and velocity of the proton).

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