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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential VV and then made to describe semi-circular paths of radius RR using a magnetic field BB. If VV and BB are kept constant, the ratio of (Charge on the ionMass of the ion)\left(\frac{\text{Charge on the ion}}{\text{Mass of the ion}}\right) (qm)\left(\frac{q}{m}\right) will be proportional to:

A

1R\frac{1}{R}

B

1R2\frac{1}{R^2}

C

R2R^2

D

RR

Step-by-Step Solution

  1. Acceleration by Electric Field: When an ion with charge qq and mass mm is accelerated from rest through a potential difference VV, the work done by the electric field equals the gain in kinetic energy. qV=12mv2  ⟹  v=2qVmqV = \frac{1}{2}mv^2 \implies v = \sqrt{\frac{2qV}{m}}
  2. Motion in Magnetic Field: Upon entering a uniform magnetic field BB perpendicular to its velocity, the Lorentz force provides the necessary centripetal force for circular motion . qvB=mv2R  ⟹  v=qBRmqvB = \frac{mv^2}{R} \implies v = \frac{qBR}{m}
  3. Relating Specific Charge (q/m) to R: Substitute the expression for velocity (vv) from the magnetic field equation into the energy equation: qV=12m(qBRm)2qV = \frac{1}{2}m \left( \frac{qBR}{m} \right)^2 qV=12mq2B2R2m2qV = \frac{1}{2}m \frac{q^2 B^2 R^2}{m^2} V=12qB2R2mV = \frac{1}{2} \frac{q B^2 R^2}{m} Rearranging to find the charge-to-mass ratio (q/mq/m): qm=2VB2R2\frac{q}{m} = \frac{2V}{B^2 R^2}
  4. Conclusion: Since VV and BB are constant, the specific charge is inversely proportional to the square of the radius . qm∝1R2\frac{q}{m} \propto \frac{1}{R^2}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOVING CHARGES AND MAGNETISM. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMOVING CHARGES AND MAGNETISMspectrometermeasuringmassesinitiallyaccelerated

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