Magnetic Effects & Magnetism

JEE Main level, single correct, medium

141 of 276

Question 141 of 276

A proton, a deuteron and an α\alpha-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

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Answer: (B) 1:2:11:\sqrt{2}:1

Radius of circular path in magnetic field is given by
R=mvqB=m(2(KE))qBm∝mqR=\dfrac{mv}{qB}=\dfrac{m\left(\sqrt{2\left(KE\right)}\right)}{qB\sqrt{m}}\propto \dfrac{\sqrt{m}}{q}
RP:RD:Rα=11:21:42=1:2:1{R}_{P}:{R}_{D}:{R}_{\alpha }=\dfrac{1}{1}:\dfrac{\sqrt{2}}{1}:\dfrac{\sqrt{4}}{2}=1:\sqrt{2}:1

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