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Physics · Moving Charges and Magnetic Field

JEE Main 2024 — 29 January, Shift 2 — Question 38

Two particles XX and YY having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii R1\mathrm{R}_{1} and R2\mathrm{R}_{2} respectively. The mass ratio of X and Y is :

  1. Option A:

    (R2R1)2\left(\frac{R_{2}}{R_{1}}\right)^{2}

  2. Option B:

    (R1R2)2\left(\frac{R_{1}}{R_{2}}\right)^{2}

    Correct
  3. Option C:

    (R1R2)\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)

  4. Option D:

    (R2R1)\left(\frac{R_{2}}{R_{1}}\right)

Answer: B

Step-by-step solution

R=mvqB=pqB=2 m(KE)qB=2mqVqB\mathrm{R}=\frac{\mathrm{mv}}{\mathrm{qB}}=\frac{\mathrm{p}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{~m}(\mathrm{KE})}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{mqV}}}{\mathrm{qB}} R∝m\mathrm{R} \propto \sqrt{\mathrm{m}}

m∝R2\mathrm{m} \propto \mathrm{R}^{2}

m1 m2=(R1R2)2\frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{2}

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
29 January, Shift 2
Subject
Physics
Chapter
Moving Charges and Magnetic Field
Topic
Motion of Charged Particles in magnetic Fields

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