Physics (2018) | JEE 2018 | Discussion Page

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_e,r_p,rα is repectively, in a unifrom magnetic field B. The relation between r_e,r_p, r_α is>>

$r_{e}\gt r_{p}= r_{\alpha}$

$r_{e}\lt r_{p}= r_{\alpha}$

$r_{e}\lt r_{p}\lt r_{\alpha}$

$r_{e}\lt r_{\alpha}\lt r_{p}$

Answer:

Option B

Explanation:

From $Bqv=\frac{mv^{2}}{r},$ we have

$r=\frac{mv}{Bq}=\frac{\sqrt{2mK}}{Bq}$

where,K is the kinetic energy

As, kinetic energies of particles are same ;

$r\propto \frac{\sqrt{m}}{q}$

= $r_{e}:r_{p}:r_{\alpha}=\frac{\sqrt{m}_{e}}{e}:\frac{\sqrt{m_{p}}}{e}:\frac{\sqrt{4m_{p}}}{2e}$

Clearly, $r_{p}=r_{\alpha}$ and $r_{e}$ , is least [ $\because m _{e}<m_{p}$ ]

So, $r_{p} =r_{\alpha}>r_{e}$

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Answer:

Explanation: