Question

The y component of the electric field of an electromagnetic wave travelling in the +x direction through vacuum obeys the equation Ey = (375 N/C) cos [kx − (2.20 × 10 14 rad/s)t]. What is the wavelength of this electromagnetic wave?a. 0.272 μmb. 1.36 μmc. 2.72 μmd. 8.57 μme. 17.1 μm

Answer 1

λ =8.57 μ m

Step-by-step explanation:

Given that

Ey = 375 cos [kx − (2.20 × 10¹⁴ rad/s)t] N/C

Standard form

Ey=Eo cos[k x-ωt] N/C

By comparing the given equation with the standard wave equation

Eo = 375 N/C

ω = 2.20 × 10¹⁴ rad/s

We know that ω = 2 π f

`f=(\omega)/(2\pi )`

`f=(2.2* 10^(14))/(2\pi )\ Hz`

f=3.50×10¹³ Hz

We know that the velocity given as

V = f λ

λ =Wavelength

V=Speed = 3 x 10⁸ m/s

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

`\lambda =(3* 10^8)/(3.5* 10^(13))\ m`

λ =0.00000857 m ( 1 μ m = 10⁶ m)

λ =8.57 μ m