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?

Question

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? (A) E=( hatn× B/c) (B) E=-c hatn× B (C) E=( hatn× E/c) (D)  hatn× E× B=0

Tardigrade Admin · Accepted Answer

As (E/B)=c, for an electromagnetic wave, relation E=( hatn× B/c) is dimensionally incorrect.

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

$E = - c \overset{n}{^} \times B$

$E = \frac{n ^ \times E}{c}$

$\overset{n}{^} \times E \times B = 0$

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

Q. A plane electromagnetic wave propagating in the direction of the unit vector 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=cn^×B​

E=−cn^×B

E=cn^×E​

n^×E×B=0

As BE​=c, for an electromagnetic wave, relation E=cn^×B​ is dimensionally incorrect.

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

$E = - c \overset{n}{^} \times B$

$E = \frac{n ^ \times E}{c}$

$\overset{n}{^} \times E \times B = 0$

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