A) Trajectory of electron is less curved
B) Trajectory of proton is less curved
C) Both trajectories are equally curved
D) Both move on straight line path
Correct Answer: A
Solution :
When a charged particle enters a magnetic field perpendicularly, it moves on a circular path. The required centripetal force is provided by magnetic force. \[ie,\] Magnetic force = Centripetal force. or \[qvB=\frac{m{{v}^{2}}}{r}\] \[\therefore \] \[r=\frac{mv}{qB}\] ? (i) Now kinetic energy of the particle, \[K=\frac{1}{2}m{{v}^{2}}\] \[\Rightarrow \] \[mv=\sqrt{2mK}\] Therefore, Eq. (i) becomes \[r=\frac{\sqrt{2mK}}{qB}\] or \[r\propto \sqrt{m}\] \[\therefore \] \[\frac{{{r}_{e}}}{{{r}_{p}}}=\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}\] As\[{{m}_{e}}<{{m}_{p}}\]; so\[{{r}_{e}}<{{r}_{p}}\]. Hence, trajectory of electron is less curved.
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