Question

The y-component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation ey=(375n/c)cos[kxâ(2.20Ã1014rad/s)t]. (c=3.0Ã108m/s) what is the largest that the x-component of the wave can be?

Answer 1

Answer:1.25 *10^-6

Explanation: As if we take that 375 is the Emax, and that in order to find the largest that the x-component can be, we need to find Bmax. E=Bc

375=B*3*10^8

375/(3*10^8)=B

B=1.25 *10^-6 T, or 1.25 μT

Answer 2

Ey = 375 cos [ kx - (92.20x10^14).t ]

the formula of the electric field of an electromagnetic wave :
=> Ey = Emax cos (k x - ω t)
=> Ey = Emax cos [(2π/λ) - (2π f).t ]

then : (2π f).t = (92.20x10^14).t
===> 2π f = 92.20x10^14
===> f = 92.20x10^14 / 2π
===> f = 1.46 x 10^15 hertz

the speed of electromagnetic wave : c = 3 x10^8 m/s

then : c = f λ
======> λ = c / f
======> λ = 3 x10^8 / 1.46 x 10^15
======> λ = 2.0547 x 10^-7 meters = 0.205 μm