Question

An electromagnetic wave going through vacuum is described by
E = E₀ sin (kx − ωt); B = B₀ sin (kx − ωt).
Then,
(a) E₀ k = B₀ ω
(b) E₀ B₀ = ωk
(c) E₀ ω = B₀ k
(d) None of these

Answer 1

(a) E₀ k = B₀ ω

The relation between E₀ and B₀ is given by $\frac{E_0}{B_0}=c$ ...(1)
Here, c = speed of the electromagnetic wave
The relation between ​ω (the angular frequency) and k (wave number):
$\frac{\omega }{k}=c$ ...(2)
Therefore, from (1) and (2), we get:
$\frac{E_0}{B_0}=$$\frac{\omega }{k}=c$
$\Rightarrow E_{0}k=B_0\omega$