Magnetic Effects & Magnetism

JEE Main level, single correct, medium

144 of 276

Question 144 of 276

Two ions having same mass have charges in the ratio 1:21:2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2:32:3. The ratio of the radii of their circular trajectories is,

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Answer: (B) 4:34:3

R=mvqB⇒R1R2=mv1q1Bmv2q2B=v1q1×q2v2=q2q1×v1v2R=\dfrac{mv}{qB}\Rightarrow \dfrac{{R}_{1}}{{R}_{2}}=\dfrac{\dfrac{m{v}_{1}}{{q}_{1}B}}{\dfrac{m{v}_{2}}{{q}_{2}B}}=\dfrac{{v}_{1}}{{q}_{1}}\times \dfrac{{q}_{2}}{{v}_{2}}=\dfrac{{q}_{2}}{{q}_{1}}\times \dfrac{{v}_{1}}{{v}_{2}}
=21×(23)=43=\dfrac{2}{1}\times \left(\dfrac{2}{3}\right)=\dfrac{4}{3}

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