Question

The magnitude of magnetic field required to accelerate protons (mass = $1.67\times {10}^{-27}kg$) in a cyclotron that is operated at an oscillator frequency 10 MHz is approximately

• A. 0.65 T
• B. 1.30 T
• C. 0.85 T
• D. 1.70 T

Answer 1

The correct option is A 0.65 T

$\text{Given}:$ mass of proton= $1.67\times {10}^{-27}$

f= 10MHz=$10\times {10}^6$Hz

$\text{Solution}:$

The frequency of cyclotron is given by,

f=$\frac{Bq}{2\pi m}$

Hence,

B=$\frac{f2\pi m}{q}$=$\frac{10\times {10}^6\times 2\times 3.14\times 1.67\times {10}^{-27}}{1.6\times {10}^{-19}}$=0.65 T

$\text{Hence A is the correct option}$