Question

An electron of mass $m$ and charge $q$ is travelling with a speed $v$ along a circular path of radius $r$ at right angles to a uniform magnetic field $B$. If speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of

• A. $\frac{r}{4}$
• B. $\frac{r}{2}$
• C. $2r$
• D. $4r$

Answer 1

The correct option is D $4r$

The magnetic force on the electrom provides the centripetal force, so, we have,

$Bqv=\frac{m{v}^2}{R}\Rightarrow R=\frac{mv}{Bq}$

So, if velocity is doubled and magnetic field intensity is halved, then the radius will become 4 times.