Physics-
General
Easy

Question

A circular metal plate of radius Ris rotating with a uniform angular velocityomegawith its plane perpendicular to a uniform magnetic field B. Then the emf developed between the centre and the rim of the plate is

  1. pi omega B R to the power of 2 end exponent  
  2. omega B R to the power of 2 end exponent  
  3. pi omega B R to the power of 2 end exponent divided by 2  
  4. omega B R to the power of 2 end exponent divided by 2  

The correct answer is: omega B R to the power of 2 end exponent divided by 2


    From Faraday’s law of electromagnetic induction, the emf induced between center and rim is equal to rate of change of magnetic flux.

    e equals negative fraction numerator d ϕ over denominator d t end fraction
    Where, d ϕ equals B d A commawhere B is magnetic field and d A the area.
    therefore blank e equals negative fraction numerator B not stretchy integral from 0 to R of d A over denominator T end fraction
    e equals negative fraction numerator B cross times pi R to the power of 2 end exponent over denominator T end fraction
    Also, omega equals fraction numerator 2 pi over denominator T end fraction comma where T is periodic time,
    e equals negative fraction numerator B pi R to the power of 2 end exponent over denominator 2 pi divided by omega end fraction
    blank equals blank minus fraction numerator B R to the power of 2 end exponent omega over denominator 2 end fraction

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