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Q.
An electron and a proton enters in a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is correct?
Moving Charges and Magnetism
Solution:
Charged particle enters in magnetic field perpendicularly it moves in circular path. Therequired centripetal force is provided by magnetic force.
$r =\frac{ m v }{ B q }$
Kinetic energy of the particle
$K =\frac{1}{2} mv ^{2} \Rightarrow mv =\sqrt{2 mK }$
$r =\frac{\sqrt{2 mK }}{ qB }$
$r \propto \sqrt{ m }$
$\frac{r_{e}}{r_{p}}=\sqrt{\frac{m_{e}}{m_{p}}}$
So, $m_{e}<\,m_{p}$
$r_{e}<\,r_{p}$
Trajectory of electron is more curved and trajectory of proton is less curved.