Answer the following:
(a) Write the expression for the force `vec(F)` acting on a particle of mass m and charge q moving with velocity`vecV` in a magnetic field `vecB` . Under what conditions will it move in
(i) a circular path and (ii) a helical path ?
(b) Show that the kinetic energy of the particle moving a magnetic field remains constant.

Explanation

### Step-by-Step Solution

**(a)** **Expression for the Force on a Charged Particle in a Magnetic Field**

The force \(\vec{F}\) acting on a particle of mass \(m\) and charge \(q\) moving with velocity \(\vec{V}\) in a magnetic field \(\vec{B}\) is given by the Lorentz force law:

\[
\vec{F} = q (\vec{V} \times \vec{B})
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