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Electrostatic Potential And Capacitance

Question
CBSEENPH12040040

The electric potential at a point in free space due to a charge Q coulomb is Q x 1011 V. The electric field at that point is

  • 4 space πε subscript straight o space straight Q space straight x space 10 to the power of 22 space straight V divided by straight m
  • 12 πε subscript straight o straight Q space straight x space 10 to the power of 20 space straight V divided by straight m
  • 4 πε subscript straight o straight Q space straight x space 10 to the power of 20 space straight V divided by straight m
  • 12 space πε subscript straight o space straight Q space straight x space 10 to the power of 22 space straight V divided by straight m

Solution

A.

4 space πε subscript straight o space straight Q space straight x space 10 to the power of 22 space straight V divided by straight m

Search for the relations of electric potential and electric field at particular point. At any point, electric potential due to charge Q is 
straight V space equals space fraction numerator 1 over denominator 4 space πε subscript straight o end fraction. straight Q over straight r space space..... space left parenthesis straight i right parenthesis space
where r is the distance of observation point from the charge.
At the same point, electric field is 
straight E space equals space fraction numerator 1 over denominator 4 space straight pi space straight epsilon subscript straight o end fraction. straight Q over straight r squared space... space left parenthesis ii right parenthesis
combining space Eqs. space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space have
straight E space equals space fraction numerator 4 πε subscript straight o straight V squared over denominator straight Q end fraction space equals space fraction numerator 4 πε subscript straight o space straight x space left parenthesis straight Q space straight x space 10 to the power of 11 right parenthesis squared over denominator straight Q end fraction
space equals space 4 πε subscript straight o straight Q space straight x space 10 to the power of 22 space straight V divided by straight m

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