The radius of curvature of the path of a char | vedclass

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(D) When a charged particle with charge $q$,mass $m$,and velocity $v$ moves in a uniform magnetic field $B$ perpendicular to its motion,it experiences

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Both $(b)$ and $(c)$

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(D) When a charged particle with charge $q$,mass $m$,and velocity $v$ moves in a uniform magnetic field $B$ perpendicular to its motion,it experiences a magnetic Lorentz force $F = qvB$.This force provides the necessary centripetal force for circular motion: $qvB = \frac{mv^2}{r}$.Rearranging for the radius $r$,we get $r = \frac{mv}{qB}$.Since linear momentum $P = mv$,the expression becomes $r = \frac{P}{qB}$.From this formula,it is clear that $r$ is directly proportional to the linear momentum $P$ and inversely proportional to the magnetic field $B$.Therefore,both statements $(b)$ and $(c)$ are correct.

The radius of curvature of the path of a charged particle moving in a static uniform magnetic field is

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