Question

In a plane electromagnetic wave, the direction of electric field and magnetic field are represented by `hat"k"` and 2`hat"i" - 2hat"j"`, respectively. What is the unit vector along direction of propagation of the wave.

Options

• `1/sqrt2(hat"i" + hat"j")`

• `1/sqrt2(hat"j" + hat"k")`

• `1/sqrt5(hat"i" + hat2"j")`

• `1/sqrt5(hat2"i" + hat"j")`

Answer 1

`bb(1/sqrt2(hat"i" + hat"j"))`

Explanation:

The direction of the electric and magnetic fields will not affect how an electromagnetic wave propagates.

`hat"C"=hat"E"xxhat"B"`

Here unit vector `hat"C"` is perpendicular to both `hat"E"` and `hat"B"`

Given, `vec"E"=hat"k", vec"B" = 2hat"i" - 2hat"j"`

∴ `hat"C"=hat"E"xxhat"B"`

= `1/sqrt2|(hat"i"     hat"j"     hat"k"), (0    0   1),(1 (-1)  0)|`

= `(hat"i"+hat"j")/sqrt2`

⇒ `hat"C" = (hat"i"+hat"j")/sqrt2`