Question

A charged particle of mass m charge q moving at a uniform velocity v enters a uniform magnetic field B normal to the field direction. Deduce an expression for Kinetic Energy of the particle. Why does the Kinetic Energy of the charged particle not change when moving through the magnetic field?

Answer 1

We know the force on charge particle
$\overrightarrow{F}=q\left(\overrightarrow{v}\times \overrightarrow{B}\right)$
And this force is provided by
$$\begin{gathered} \frac{m{v}^2}{r} \\ So,qvB=\frac{m{v}^2}{r} \\ v=\frac{qBr}{m}iscons\tan t. \\ Thuskineticenergyiscons\tan t. \\ Andkineticenergy=\frac{1}{2}m{v}^2=\frac{(qBr{)}^2}{2m} \end{gathered}$$