Magnetic Effects & Magnetism

JEE Main level, single correct, medium

145 of 276

Question 145 of 276

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let rd{r}_{d} and rα{r}_{\alpha } be their respective radii of circular path. The value of rdrα\dfrac{{r}_{d}}{{r}_{\alpha }} is equal to:

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Answer: (B) 2\sqrt{2}

r=mvqB=2mkqBr=\dfrac{mv}{qB}=\dfrac{\sqrt{2mk}}{qB}
rdrα=mdmαqαqd=24(21)=2\dfrac{{r}_{d}}{{r}_{\alpha }}=\sqrt{\dfrac{{m}_{d}}{{m}_{\alpha }}}\dfrac{{q}_{\alpha }}{{q}_{d}}=\sqrt{\dfrac{2}{4}}\left(\dfrac{2}{1}\right)=\sqrt{2}
Hence option (2).(2).

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