$A$ 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).

  • A
    $\frac{2 \pi n m}{q}, \frac{q v B r}{2}$
  • B
    $\frac{\pi n m}{q}, \frac{q v B r}{2}$
  • C
    $\frac{2 \pi n m}{q}, q v B r$
  • D
    $\frac{4 \pi n m}{q}, \frac{q v B r}{2}$

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$A$ cyclotron is used to accelerate

$A$ cyclotron's oscillator frequency is $20 MHz$. The operating magnetic field for accelerating protons is (charge of proton $= 1.6 \times 10^{-19} C$,mass of proton $= 1.67 \times 10^{-27} kg$). (in $T$)

If the maximum value of accelerating potential provided by a radio frequency oscillator is $12 \, kV$,the number of revolutions made by a proton in a cyclotron to achieve one-sixth of the speed of light is ....... .
$[m_p = 1.67 \times 10^{-27} \, kg, e = 1.6 \times 10^{-19} \, C, c = 3 \times 10^8 \, m/s]$

$A$ charged particle is subjected to acceleration in a cyclotron as shown. The charged particle undergoes an increase in its speed:

In a cyclotron,the time taken by an ion to describe a semicircular path in a dee is

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