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Current Electricity

Question
CBSEENPH12039853
Wired Faculty App

The electric field associated with an electromagnetic wave in vacuum is given by E=i 40 cos (kz-6x108t), where E, z= and t are in volt/m, metre and second respectively. The value of wave vector k is

  • 2 m-1

  • 0.5 m-1

  • 6 m-1

  • 3 m-1

Solution

A.

2 m-1

Electromagnetic wave equation 
straight E space equals space straight E subscript straight o space cos space left parenthesis kz minus ωt right parenthesis Speed space of space electromagnetic space wave space straight v space equals space straight omega over straight k space Given space equation straight E space equals space straight i 40 space cos space left parenthesis kz minus 6 space straight x space 10 to the power of 8 space straight t right parenthesis comparing space Eqs. space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get straight omega space equals space 6 space straight x space 10 to the power of 8 and straight E subscript straight o space equals 40 space straight i here comma space wave space factor space straight k space equals space straight omega over straight v space equals space fraction numerator 6 space straight x space 10 to the power of 8 over denominator 3 straight x space 10 to the power of 8 end fraction space equals space 2 space straight m to the power of negative 1 end exponent

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