Question

In SI units, the electric field in an electromagnetic wave is described by Ey = 112 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. Hz

Answer 1

Step-by-step explanation:

The electric field in an electromagnetic wave is described by:

`E_y=112\ sin(1.4* 10^7x-\omega t)`

The general equation is given by :

`E=E_0\ sin(kx-\omega t)`

Here,

The amplitude in electric field is
`E_0=112`

Propagation constant,
`k=1.4* 10^7`

`\omega` is the angular frequency

(a) The amplitude of the corresponding magnetic field oscillations is given by :

`B_0=(E_0)/(c)`

`B_0=(112)/(3* 10^8)`

`B_0=3.73* 10^(-7)\ T`

`B_0=0.37\ \mu T`

(b) We know that the propagation constant is given by :

`k=(2\pi)/(\lambda)`

`\lambda=(2\pi)/(k)`

`\lambda=(2\pi)/(1.4* 10^7)`

`\lambda=4.48* 10^(-7)\ m`

`\lambda=0.44\ \mu T`

(c)
`f=(c)/(\lambda)`

`f=(3* 10^8\ m/s)/(4.48* 10^(-7)\ m)`

`f=6.69* 10^(14)\ Hz`