Physics-
General
Easy

Question

The diameter of each plate of an air capacitor is 4 c m. To make the capacity of this plate capacitor equal to that of 20 c m diameter sphere, the distance between the plates will be

  1. 4 cross times 1 0 to the power of negative 3 end exponent m    
  2. 1 cross times 1 0 to the power of negative 3 end exponent m    
  3. 1 c m    
  4. 1 cross times 1 0 to the power of negative 3 end exponent c m    

The correct answer is: 1 cross times 1 0 to the power of negative 3 end exponent m


    Capacity of spherical conductor of 20 cm diameter C subscript 1 end subscript equals 4 pi epsilon subscript 0 end subscript r equals 4 pi epsilon subscript 0 end subscript cross times 10
    Capacity of parallel plate air capacitor
    C subscript 2 end subscript equals fraction numerator epsilon subscript 0 end subscript A over denominator d end fraction equals fraction numerator epsilon subscript 0 end subscript left square bracket pi left parenthesis 2 right parenthesis to the power of 2 end exponent right square bracket over denominator d end fraction equals fraction numerator epsilon subscript 0 end subscript cross times 4 pi over denominator d end fraction
    Hence C subscript 1 end subscript equals C subscript 2 end subscript Þ 40 pi epsilon subscript 0 end subscript equals fraction numerator 4 pi epsilon subscript 0 end subscript over denominator d end fractionÞ d equals 1 0 to the power of negative 3 end exponent m

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