Question

Show that the kinetic energy of the particle moving in a magnetic field remains constant.

Answer 1

When a charged particle having charge q moves inside a magnetic field `vecB` with velocity v, it experiences a force `vecF =q(vecV ×vecB)`.

From the formula of the force we can see that, `vecF`is always perpendicular to both `vecV` and `vecB`, thus in this case work done by the force is always zero. From, the work energy theorem we know that the change in the kinetic energy of the body is equal to the work done.

Change in kinetic energy = 0
⇒Kinetic energy = A constant