Question

In si units, the electric field in an electromagnetic wave is described by ey = 104 sin(1.40 107x − ωt). (a) find the amplitude of the corresponding magnetic field oscillations. µt (b) find the wavelength λ. µm (c) find the frequency f.

Answer 1

Answers:
(a)
`B_o  = 0.3466`μT
(b)
`\lambda = 0.4488`μm
(c) f =
`6.68 * 10^(14)Hz`

Step-by-step explanation:
Given electric field(in y direction) equation:

`E_y = 104sin(1.40 * 10^7 x -\omega t)`

(a) The amplitude of electric field is
`E_o = 104`. Hence

The amplitude of magnetic field oscillations is
`B_o = (E_o)/(c)`
Where c = speed of light

Therefore,

`B_o = (104)/(3*10^8) = 0.3466`μT (Where T is in seconds--signifies the oscillations)

(b) To find the wavelength use:

`(2 \pi )/(\lambda) = 1.40 * 10^7`

`\lambda = (2 \pi)/(1.40) * 10^(-7)`

`\lambda = 0.4488`μm

(c) Since c = fλ
=> f = c/λ

Now plug-in the values
f = (3*10^8)/(0.4488*10^-6)
f =
`6.68 * 10^(14)Hz`