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  4. 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?

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Q. 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?

KVPYKVPY 2009Electromagnetic Waves

Solution:

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