(10%) Problem 10: The electric field in an electromagnetic wave is in the y -dir

Question

(10%) Problem 10: The electric field in an electromagnetic wave is in the y -direction and described by Ey = E0 cos(kx ? omega t), where E0= 265 N/C Randomized Variables E0= 265 N/C 25% Part (a) If the electromagnetic wave is traveling in the x -direction in vacuum, what is the direction of the magnetic field? 25% Part (b) Express the amplitude of the magnetic field, B0, in terms of E0 and the speed of light c. 25% Part (c) Find the intensity of the electromagnetic wave, I, in terms of E() c, and the vacuum susceptibility & mu 0. 25% Part (d) Solve for the numerical value of! in watts per square meter.

Explanation / Answer

Ey=Eo*cos(Kx-Wt)
Eo=265 N/C

a)

here

Elecrtic fild is along y-direction

wave traveling along x-direction

magnetic field must be perpendicular to both x and y

hence magnetic field must be along Z-directon

b)

Bo=Eo/c

c)

the electomagnetic wave energy density

u=(1/2)*eo*Eo^2

or

u=(1/2uo)*Bo^2

now,

inetsity is energy crossing per unit area per unit time

I=u*c

I=(1/2)*eo*Eo^2*c

=(1/2)*(eoc)*Eo^2

=(1/2)*(1/uo*c)*Eo^2

I=(1/2uo*c)*Eo^2

=(Eo^2)/2uo*c

d)

I=(265^2)/(2*4*3.14*10^-7*3*10^8)

=93.186 W/m^2

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