question_answer

When a charged particle, travelling with uniform speed enters a uniform magnetic field perpendicularly then, its kinetic energy:

A)  remains constant

B)  increases

C)   decreases

D)   becomes zero

Correct Answer: A

Solution :

Key Idea: Force due to magnetic field provides the required centripetal force. The force due to magnetic field \[B\] is                 \[F=qvB\sin \theta \]                                     ... (i) When particle with charge\[q\]enters perpendicularly then\[\theta ={{90}^{o}}\], so\[F=qvB\]and required centripetal force is                 \[F=\frac{m{{v}^{2}}}{r}\]                                            ... (ii) From Eqs. (i)-and (ii), we get                 \[\frac{m{{v}^{2}}}{r}=qvB\] \[\Rightarrow \]               \[v=\frac{qrB}{m}\] Kinetic energy\[K=\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{\left( \frac{qrB}{m} \right)}^{2}}\]                 \[=\frac{{{q}^{2}}{{r}^{2}}{{B}^{2}}}{2m}=\]constant Hence, kinetic energy remains constant.