Question

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
(a) the velocity
(b) the momentum
(c) the kinetic energy
(d) none of these.

Answer 1

The answer is (c) the kinetic energy.

Explanation:

The particle of mass m carries charge q. This is projected in a plane at the speed v perpendicular to the magnetic field B that is uniform. The field is inclined to bounce the particle in a rounded path with radius r.

Therefore, mv2r = qvB⇒ r = mvqB

Now, Area, A = πr2 ⇒A = kv2

Here, k = πmqB2

A particle’s kinetic energy, E = 12mv2

Therefore, the bounded area is proportional to the kinetic energy.