A plane electromagnetic wave propagating in t | vedclass

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Question

(A) For a plane electromagnetic wave,the relationship between the electric field $E$ and the magnetic field $B$ is given by $E = c(B 	imes \hat{n})$

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) For a plane electromagnetic wave,the relationship between the electric field $E$ and the magnetic field $B$ is given by $E = c(B 	imes \hat{n})$ or $B = \frac{1}{c}(\hat{n} 	imes E)$.Dimensional analysis shows that $[E] = [B][c]$.In option $A$,the expression is $E = \frac{\hat{n} 	imes B}{c}$. The dimensions of the right-hand side are $\frac{[B]}{[c]} = \frac{[B]}{[L/T]} = [B][T/L]$.Since $[E] = [B][L/T]$,the dimensions do not match.Therefore,the relation $E = \frac{\hat{n} 	imes B}{c}$ is dimensionally incorrect.

$A$ 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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