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 \[{{r}_{\alpha }}={{r}_{p}}\,<{{r}_{d}}\]You need to login to perform this action.
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