MCQ
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?
  • $E =\frac{\hat{ n } \times B }{c}$
  • B
    $E =-c \hat{ n } \times B$
  • C
    $B =\frac{\hat{ n } \times E }{c}$
  • D
    $\hat{n} \times E \times B=0$

Answer

Correct option: A.
$E =\frac{\hat{ n } \times B }{c}$
a
(a)

As $\frac{E}{B}=c$, for an electromagnetic wave, relation $E =\frac{\hat{ n } \times B }{c}$ is dimensionally incorrect.

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