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Question
An electromagnetic wave travelling along z-axis is given as: E = E0 cos (kz – ωt.). Choose the correct options from the following;
- The associated magnetic field is given as `B = 1/c hatk xx E = 1/ω (hatk xx E)`.
- The electromagnetic field can be written in terms of the associated magnetic field as `E = c(B xx hatk)`.
- `hatk.E = 0, hatk.B` = 0.
- `hatk xx E = 0, hatk xx B` = 0.
Options
a, b and c
a, c and d
b, c and d
b and d
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Solution
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`
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