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Magnetics question

2021 · 25 Jul · Shift 2 · Q51
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Magnetics question

2021 · 25 Jul · Shift 2 · Q51

JEE MainPhysicsMagneticsMCQ+4 / −1
Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :
  1. A
    1 : 4
  2. B
    4 : 3
  3. C
    3 : 1
  4. D
    2 : 3
View written solutionFree

Correct answer: B

  1. Use the formula for radius in a magnetic field

    For a charged particle moving perpendicular to a uniform magnetic field, r=mvqBr = \frac{mv}{qB}r=qBmv​

  2. Identify the given ratios

    • Masses are same: m1=m2m_1 = m_2m1​=m2​
    • Charges are in the ratio: q1:q2=1:2q_1 : q_2 = 1 : 2q1​:q2​=1:2
    • Speeds are in the ratio: v1:v2=2:3v_1 : v_2 = 2 : 3v1​:v2​=2:3

  3. Write the ratio of radii

    Since r∝vqr \propto \frac{v}{q}r∝qv​ (because mmm and BBB are same), r1r2=v1/q1v2/q2=v1q2v2q1\frac{r_1}{r_2} = \frac{v_1/q_1}{v_2/q_2} = \frac{v_1 q_2}{v_2 q_1}r2​r1​​=v2​/q2​v1​/q1​​=v2​q1​v1​q2​​

  4. Substitute the ratios

    r1r2=2×23×1=43\frac{r_1}{r_2} = \frac{2 \times 2}{3 \times 1} = \frac{4}{3}r2​r1​​=3×12×2​=34​

    Therefore, r1:r2=4:3r_1 : r_2 = 4 : 3r1​:r2​=4:3

  5. Match with the options

    The correct option is: B: 4:34:34:3

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