A particle is projected into a plane perpendicular to a uniform magnetic field. The area enclosed by the path traced by the particle is proportional to

Step-by-step solution

When a charged particle is projected perpendicular to a uniform magnetic field, it moves in a circular path of radius r = mv qB . The area enclosed by this circular path is A = r^2 = ( mv qB )^2 = m^2 v^2 q^2 B^2 . The kinetic energy of the particle is K = 1 2 m v^2 , which gives m^2 v^2 = 2mK . Substituting this in the expression for area, we get: A = 2 m K q^2 B^2 Since m , q , and B are constants, A K . Thus, the area enclosed by the path is directly proportional to the kinetic energy of the particle.