A cyclotron operates with a given magnetic field and at a given frequency. If "R" denotes the radius of the final orbit, the energy of the particle is proportional to:
Correct answer: B. R2
- A. 1/R
- B. R2
- C. R
- D. R3
Explanation
The kinetic energy of the particle is KE = (1/2)mv². The speed of the particle at radius R is given by v = qBR/m. Substituting this into the KE equation gives KE = (1/2)m(qBR/m)² = (q²B²R²)/(2m). Since q, B, and m are constants, the kinetic energy is directly proportional to R².
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Magnetic flux density and magnetic flux describe the strength of a magnetic field and the field passing through a surface. A charged particle moving through a magnetic field experiences a force perpendicular to its velocity and may follow circular or helical motion, depending on the angle between velocity and field.
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