A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to

If a charged particle is projected with velocity v on a plane perpendicular to a uniform magnetic field B, then the particle will travel in a circle. Whose radius is where m and q are the mass and the charge of the particle respectively.

So the area enclosed by the path will be A = ϖR² = = = kinetic energy

Thus, the area will be proportional to the kinetic energy of the particle.