A plane electromagnetic wave propagating in the direction of the unit vector $\hat{ n }$ with a speed $c$ is described by electric and magnetic field vectors $E$ and $B$, respectively. Which of the following relations (in $SI$ units) between $E$ and $B$ can be ruled out on dimensional grounds alone?

  • [KVPY 2009]
  • A

    $E =\frac{\hat{ n } \times B }{c}$

  • B

    $E =-c \hat{ n } \times B$

  • C

    $B =\frac{\hat{ n } \times E }{c}$

  • D

    $\hat{n} \times E \times B=0$

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