The magnitude of the magnetic field required to accelerate protons (mass =1.67 × 10-27 kg ) in a cyclotron that is operated at an oscillator frequency 12 MHz is approximately

Question

The magnitude of the magnetic field required to accelerate protons (mass =1.67 × 10-27 kg ) in a cyclotron that is operated at an oscillator frequency 12 MHz is approximately (A) 0.8 T (B) 1.6 T (C) 2.0 T (D) 3.2 T

Tardigrade Admin · Accepted Answer

The cyclotron frequency, v=(q B/2 π m) Magnetic field B =(2 π m v/q) B =(2 × 3.14 × 1.67 × 10-27 × 12 × 106/1.6 × 10-19) =78.6 × 10-2 T B =0.8 T

Q. The magnitude of the magnetic field required to accelerate protons (mass $= 1.67 \times 1 0^{- 27} k g$ ) in a cyclotron that is operated at an oscillator frequency $12 M Hz$ is approximately

0.8 T

1.6 T

2.0 T

3.2 T

The cyclotron frequency, $v = \frac{qB}{2 πm}$
Magnetic field $B = \frac{2 πm v}{q}$
$B = \frac{2 \times 3.14 \times 1.67 \times 1 0 ^{- 27} \times 12 \times 1 0 ^{6}}{1.6 \times 1 0 ^{- 19}}$
$= 78.6 \times 1 0^{- 2} T$
$B = 0.8 T$

Q. The magnitude of the magnetic field required to accelerate protons (mass =1.67×10−27kg ) in a cyclotron that is operated at an oscillator frequency 12MHz is approximately