Question

A cyclotron is operating at a frequency of 12 MHz. Mass and charge of deuteron are \( 3.3 \times 10^{-27} \, {kg} \) and \( 1.9 \times 10^{-19} \, {C} \). To accelerate deuteron, the necessary magnetic field is

• A. 0.16 T
• B. 1.6 T
• C. 0.016 T
• D. 16 T

Hint:

In a cyclotron, the magnetic field required to accelerate a particle is directly proportional to its mass and the operating frequency, and inversely proportional to its charge.

Answer 1

The Correct Option is B

In a cyclotron, the frequency of the particle's revolution is given by: \[ f = \frac{qB}{2\pi m} \] where \( q \) is the charge of the particle, \( B \) is the magnetic field, and \( m \) is the mass of the particle. Rearranging to solve for \( B \), we get: \[ B = \frac{2\pi m f}{q} \] Substitute the given values: \[ B = \frac{2\pi (3.3 \times 10^{-27}) (12 \times 10^6)}{1.9 \times 10^{-19}} \approx 1.6 \, {T} \] Hence, the correct answer is (b).