Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

Under the influence of a uniform magnetic field, a charged particle moves with constant speed v in a circle of radius R. The time period of rotation of the particle -

depends on v and not on R

depends on R and not on v

is independent of both v and R

depends on both v and R

Step-by-Step Solution

Force Balance: When a charged particle (mass $m$ , charge $q$ ) moves perpendicular to a magnetic field ( $B$ ), the magnetic Lorentz force provides the necessary centripetal force for circular motion. $qvB = \frac{mv^2}{R}$ .
Angular Velocity: From the force equation, we can find the angular velocity ( $\omega = v/R$ ): $\frac{v}{R} = \frac{qB}{m} \Rightarrow \omega = \frac{qB}{m}$
Time Period: The time period ( $T$ ) of rotation is derived from the angular velocity: $T = \frac{2\pi}{\omega} = \frac{2\pi m}{qB}$ .
Conclusion: The expression for the time period depends only on the mass ( $m$ ), charge ( $q$ ), and magnetic field ( $B$ ). It does not contain velocity ( $v$ ) or radius ( $R$ ). This property is fundamental to the operation of the cyclotron.

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