Step by step solution to "In a plane electromagnetic wave, the directions of..."

Damon Turner

Answered question

2022-12-30

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by

k^

and

2 i^- 2 j^

, respectively. What is the unit vector along the wave's propagation direction?
A)

\frac{1}{2} (i^+ j^)

\frac{1}{5} (2 i^+ j^)

\frac{1}{5} (i^+ 2 j^)

\frac{1}{2} (j^+ k^)

mitafiagwk

Beginner2022-12-31Added 3 answers

The correct answer is A

\frac{1}{2} (i^+ j^)

Step 1: Given data
The direction of the electric field,

E \to

k^

The direction of the magnetic field,

B \to

2 i^- 2 j^

Step 2: Formula used
The formula to find the unit vector is:

u^= \frac{u}{| u |}

u^=

unit vector

u =

non-zero vector

| u | =

magnitude (or length) of

u

The direction of the vector along the direction of propagation of the wave

= E \to \times B \to

Step 3 : Calculate the Propagation Vector

E \to \times B \to = k^\times (2 i^- 2 j^) = 2 k^\times i^- 2 k^\times j^= 2 j^+ 2 i^

The magnitude of

u

can be given as,

(u) = \frac{2 i^+ 2 j^}{2^{2}} = \frac{2 i^+ 2 j^}{22}

Step 4: Calculate the Unit Vector

U n i t v e c t o r a l o n g E \to \times B \to = \frac{1}{22} (2 i^+ 2 j^) = \frac{1}{2} (i^+ j^)

Hence, the unit vector along the direction of propagation of the wave is

\frac{1}{2} (i^+ j^)

.
Therefore, option A is correct.

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?