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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

A beam of cathode rays is subjected to crossed Electric (E) and magnetic fields (B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by:

A

B22VE2\frac{B^2}{2VE^2}

B

2VB2E2\frac{2VB^2}{E^2}

C

2VE2B2\frac{2VE^2}{B^2}

D

E22VB2\frac{E^2}{2VB^2} (where V is the potential difference between cathode and anode)

Step-by-Step Solution

  1. Velocity Selector Condition: When a charged particle (electron) moves through crossed electric (EE) and magnetic (BB) fields without deflection, the electric force (Fe=eEF_e = eE) is balanced by the magnetic force (Fm=evBF_m = evB). eE=evB⇒v=EBeE = evB \Rightarrow v = \frac{E}{B} .
  2. Energy Conservation: The electrons are accelerated by a potential difference VV between the cathode and anode. The kinetic energy gained equals the potential energy lost: 12mv2=eV\frac{1}{2}mv^2 = eV From this, the specific charge (charge-to-mass ratio) is: em=v22V\frac{e}{m} = \frac{v^2}{2V}
  3. Substitution: Substitute the expression for velocity (v=E/Bv = E/B) into the specific charge equation: em=(E/B)22V=E22VB2\frac{e}{m} = \frac{(E/B)^2}{2V} = \frac{E^2}{2VB^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 MAGNETISMcathodesubjectedcrossedelectricmagnetic

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