Question

An electromagnetic wave travelling along z-axis is given as: E = E₀ cos (kz – ωt.). Choose the correct options from the following;

1. The associated magnetic field is given as `B = 1/c hatk xx E = 1/ω (hatk xx E)`.
2. The electromagnetic field can be written in terms of the associated magnetic field as `E = c(B xx hatk)`.
3. `hatk.E = 0, hatk.B` = 0.
4. `hatk xx E = 0, hatk xx B` = 0.

पर्याय

• a, b and c

• a, c and d

• b, c and d

• b and d

Answer 1

a, b and c

Explanation:

a. The direction of propagation of an electromagnetic wave is always along the direction of vector product `vecE xx vecB`. Refer to figure.

`vecB = Bhatj = B(hatk xx hati) = E/c (hatk xx hati)`

= `1/c [k xx Ehati] = 1/c [hatk xx vecE]`  .....`("as"  E/B = c)`

b. `vecE = Ehati = cB(hatj xx hatk) = c(Bhatj xx hatk) = c(vecB xx hatk)`

c. `hatk * vecE = hatk * (Ehati)` = 0, `veck * vecB = hatk * (Bhatj)` = 0

d. `hatk xx vecE = hatk xx (Ehati) = E(hatk xx hati) = Ehatj` and `hatk xx vecB = hatk xx (Bhatj) = B(hatk xx hatj) = - Bhati`