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Question

In an oscillations of L-C circuit, the maximum charge on the capacitor is Q. The charge on the capacitor, when the energy is stored equally between the electric and magnetic field is

  1. fraction numerator Q over denominator 2 end fraction  
  2. fraction numerator Q over denominator square root of 2 end fraction  
  3. fraction numerator Q over denominator square root of 3 end fraction  
  4. fraction numerator Q over denominator 3 end fraction  

The correct answer is: fraction numerator Q over denominator square root of 2 end fraction


    Maximum energy stored in the capacitor
    U subscript m a x end subscript equals fraction numerator Q to the power of 2 end exponent over denominator 2 C end fraction
    The energy is stored equally in electric and magnetic fields
    So, energy in electric field
    E equals fraction numerator 1 over denominator 2 end fraction open parentheses fraction numerator Q to the power of 2 end exponent over denominator 2 C end fraction close parentheses
    Now, fraction numerator Q to the power of ´ 2 end exponent over denominator 2 C end fraction equals fraction numerator 1 over denominator 2 end fraction fraction numerator Q to the power of 2 end exponent over denominator 2 C end fraction
    rightwards double arrow Q to the power of ´ end exponent equals fraction numerator Q over denominator square root of 2 end fraction

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