Question

A cyclotron is operated at an oscillator frequency of $24MHz$ and has a dee radius of $60cm$ . 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 $H_1^{2}q=1.6\times 10^{-19}C$
$m=2\times 1.6\times 10^{-27}kg$
$\therefore 24\times 10^6=\frac{B\times 1.6\times 10^{-19}}{2\times 3.14\times 2\times 1.6\times 10^{-27}}$
$\Rightarrow B=\frac{2\times 3.14\times 2\times 1.6\times 10^{-27}\times 24\times \times 10^6}{1.6\times 10^{-19}}$
$=3.2T$