Question

A plane electromagnetc sinusoidal wave of frequency 40 MHz tavels free space in the x-direction. at some point and at some instant, the electric field E has its maximum value of 700 N/C and is along the y-axis. (a.) draw an illustration of the electromagnetic wve in a coordinate system, and determine the wavelength and period of the wave. (b.) calculate the magnitude and direction of the magnetic field B when E= 700 N/C in the x-direction. (c) what is the instantaneous energy density of the wave? (d) write an expression for the equation for the electric and magnetic field compnents of this electromagnetic wave.

Answer 1

given

f = 40 Mhz = 40*10^6 Hz
Emax = 700 N/c

a)

wavelength, lamda = c/f

= 3*10^8/(40*10^6)

= 7.5 m

period, T 1/f

= 1/(40*10^6)

= 2.5*10^-8 s

b) Bmax = Emax/c

= 700/(3*10^8)

= 2.33*10^-6 T

direction of B: towards +z axis

c) Energy density = epsilon*Emax^2

= 8.854*10^-12*700^2

= 4.34*10^-6 J/m^3

d) w = 2*pi*f = 2*pi*40*10^6 = 2.51*10^8 rad/s

k = 2*pi/lamda = 2*pi/7.5 = 0.838

we know,

E = Emax*sin(kx - w*t) j

= 700*sin(0.838*x - 2.51*10^8*t) j

B = Bmax*sin(kx - w*t) k