Physics-
General
Easy

Question

A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region

  1. Is zero    
  2. Decreases as fraction numerator 1 over denominator r end fraction    
  3. Increases as r    
  4. Decreases as fraction numerator 1 over denominator r to the power of 2 end exponent end fraction    

The correct answer is: Decreases as fraction numerator 1 over denominator r end fraction


    Construct a concentric circle of radius r. The induced electric field (E) at any point on the circle is equal to that at P. For this circle

    not stretchy contour integral stack E with rightwards arrow on top. d stack l with rightwards arrow on top equals open vertical bar fraction numerator d phi over denominator d t end fraction close vertical bar equals A   open vertical bar fraction numerator d B over denominator d t end fraction close vertical bar
    or E cross times left parenthesis 2 pi r right parenthesis equals pi a to the power of 2 end exponent. open vertical bar fraction numerator d B over denominator d t end fraction close vertical bar
    rightwards double arrow E equals fraction numerator a to the power of 2 end exponent over denominator 2 r end fraction open vertical bar fraction numerator d B over denominator d t end fraction close vertical bar rightwards double arrow E proportional to fraction numerator 1 over denominator r end fraction

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