JEE Main & Advanced JEE Main Online Paper (Held On 08 April 2018)

  • question_answer
    An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii \[{{r}_{e}},\,\,{{r}_{p}},\,\,{{r}_{\alpha }}\] respectively in a uniform magnetic field B. The relation between \[{{r}_{e}},\,\,{{r}_{p}},\,\,{{r}_{\alpha }}\] is:                 [JEE Main Online 08-04-2018]

    A)  \[{{r}_{e}}<{{r}_{p}}<{{r}_{\alpha }}\]                       

    B)  \[{{r}_{e}}<{{r}_{\alpha }}<{{r}_{p}}\]

    C)  \[{{r}_{e}}>{{r}_{p}}={{r}_{\alpha }}\]                       

    D)  \[{{r}_{e}}<{{r}_{p}}={{r}_{\alpha }}\]

    Correct Answer: D

    Solution :

    \[r=\frac{mv}{Bq}=\frac{\sqrt{2mk}}{Bq}\] \[\frac{{{r}_{p}}}{{{r}_{e}}}=\frac{\sqrt{{{m}_{p}}}}{\sqrt{{{m}_{e}}}}\]                  \[{{m}_{p}}>{{m}_{e}}\] \[{{r}_{p}}>{{r}_{e}}\] \[\frac{{{r}_{p}}}{{{r}_{\alpha }}}=\frac{\sqrt{{{m}_{p}}}}{{{q}_{p}}}\frac{2{{q}_{p}}}{\sqrt{4{{m}_{p}}}}=1\] \[{{r}_{p}}={{r}_{\alpha }}\]


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