Question

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 of intensity $B$. If the speed of the electron is doubled and the magnetic field is halved the resulting path would have a radius:

• A. $2r$
• B. $4r$
• C. $r / 4$
• D. $r / 2$

Answer 1

Answer: (B)

$4r$

Answer 2

The magnetic force on the electron provides the centripetal force,
so, we have, $Bqv =\frac{ mv ^{2}}{ R }$
$\Rightarrow R =\frac{ mv }{ Bq }$
So, if velocity is doubled and magnetic field intensity is halved, then the radius will become $4$ times.