A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E? [2025]

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Solution

Q.
A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E [2025]

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Ans.
(4)

$\frac{1}{2} m v^{2} = E \Rightarrow {(m v)}^{2} = 2 m E$

Also, $r = \frac{m v}{q B} \Rightarrow r = \frac{\sqrt{2 m E}}{q B}$

So, $r \propto {(E)}^{\frac{1}{2}}$

Graph should be like

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