Q 12-04-249JEE MainJEE Main 2025 (7 Apr, Shift 1)Easy
A particle of charge $q$, mass $m$ and kinetic energy $E$ enters a magnetic field perpendicular to its velocity and undergoes a circular arc of radius $r$. Which of the graphs shown in the figure represents the variation of $r$ with $E$?
Answer: (D) Graph (4)
$r = \dfrac{mv}{qB} = \dfrac{p}{qB} = \dfrac{\sqrt{2mE}}{qB}$, so $r \propto \sqrt E$.
The graph of $r$ against $E$ starts at the origin, rises steeply, and bends over (slope decreasing) like a parabola lying on its side. That is graph (4).
Solution by Sreeraj P, M.Sc Physics