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JEE Main & Advanced Sample Paper JEE Main Sample Paper-33

  • question_answer
    Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton deuteron and alpha particle are respectively \[{{\gamma }_{p}},{{\gamma }_{d}}\]and \[{{\gamma }_{\alpha }}\] then their relation will be:

    A)  \[{{\gamma }_{\alpha }}={{\gamma }_{p}}<{{\gamma }_{d}}\]

    B)     \[{{\gamma }_{\alpha }}={{\gamma }_{d}}<{{\gamma }_{p}}\]

    C)  \[{{\gamma }_{\alpha }}={{\gamma }_{d}}>{{\gamma }_{p}}\]  

    D)  \[{{\gamma }_{\alpha }}={{\gamma }_{p}}={{\gamma }_{d}}\]

    Correct Answer: A

    Solution :

    Radius of charge moving perpendicular to the magnetic field is             \[r=\frac{mv}{qB}=\frac{p}{qB}\]             But \[\frac{{{p}^{2}}}{2m}\,=k\]              \[=\,\,p=\,\sqrt{2km}\]             \[r=\frac{\sqrt{2km}}{qB}\]             \[\Rightarrow \,\,r\propto \,\frac{\sqrt{m}}{q}\]             \[{{r}_{\alpha }}\,=\frac{\sqrt{2k4m}}{2eB}\] \[{{r}_{p}}\,=\frac{\sqrt{2km}}{eB}\] \[{{r}_{d}}=\frac{\sqrt{2k2m}}{eB}\] Hence \[{{r}_{\alpha }}={{r}_{p}}\,<{{r}_{d}}\]


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