Question

A cyclotron is operated at an oscillator frequency of $ 24 \,MHz $ and has a dee radius of $ 60 \,cm $ . Find the magnitude of the magnetic field needed for deuterons to be accelerated in the cyclotron

• A. 6.4 T
• B. 3.2 T
• C. 1.6 T
• D. 0.9 T

Answer 1

Answer: (B)

The cyclotron frequency
$V=\frac{1}{T}=\frac{Bq}{2\pi m}$
For deutron $H^{2}_{1} q=1.6\times 10^{-19}C$
$m=2\times 1.6\times 10^{-27}\,kg$
$\therefore 24\times 10^{6} =\frac{B\times 1.6\times10^{-19}}{2\times 3.14\times2\times1.6\times10^{-27}}$
$\Rightarrow B=\frac{2\times3.14\times2\times1.6\times10^{-27} \times 24\times\times10^{6}}{1.6\times10^{-19}}$
$=3.2\,T$