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JEE Main & Advanced Physics EM Waves Question Bank Self Evaluation Test - Electromagnetic Waves

  • question_answer
    Which of the following is the correct equation for magnetic field as a function of x, and t where a plane electromagnetic wave propagating in the x-direction has a wavelength of 5.0 mm? The electric field is in the y-direction and its maximum value is \[30\,V{{m}^{-1}}\].        

    A) \[B={{10}^{-3}}\,\sin \,\left[ \frac{2\pi }{5\times {{10}^{-3}}}(ct-x) \right]\]

    B) \[B={{10}^{-7}}\,\sin \,\left[ \frac{2\pi }{5\times {{10}^{-3}}}(ct-x) \right]\]

    C) \[B={{10}^{-5}}\,\sin \,\left[ \frac{\pi }{1.5\times {{10}^{-3}}}(ct-x) \right]\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[E={{E}_{0}}\sin \,\omega \left( t-\frac{x}{c} \right)\];  \[B={{B}_{0}}\sin \omega \left( t-\frac{x}{c} \right)\] \[{{I}_{d}}={{I}_{0}}\sin \left( \omega t+\frac{\pi }{2} \right)=I\] and \[\omega =2\pi v=\frac{2\pi }{\lambda }c\] \[{{E}_{0}}=30\sin \left[ \frac{2\pi }{5\times {{10}^{-3}}}(ct-x) \right]\]and\[{{B}_{0}}=\frac{{{E}_{0}}}{C}={{10}^{-7}}T\] \[B={{B}_{0}}\sin \left[ \frac{2\pi }{\lambda }(ct-x) \right]={{10}^{-7}}\sin \left[ \frac{2\pi }{5\times {{10}^{-3}}}(ct-x) \right]\]


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