(10%) Problem 9: The magnetic field of an electromagnetic wave is described by B

Question

(10%) Problem 9: The magnetic field of an electromagnetic wave is described by By = B0cos(kx - omega t). where B0 = 2 x 10^-6 T and omega=8.5 x 10 ^7 rad/s. Randomized Variables B0= 2 x 1 ^-6 T omega= 8.5 x l0^7 rad/s 20% Part (a) What is the amplitude of the corresponding electric field oscillations. E0 in terms of B0? 20% Part (6) Calculate the electric field E0 in volts per meter. 20% Part (c) What is the frequency of the electromagnetic wave, f, in terms of omega? 20% Part (d) What is the wavelength of the electromagnetic wave, lambda, in terms of N and the speed of light c? 20% Part (e) Calculate the wavelength lambda in meters. Lambda=

Explanation / Answer

given

B=Bo*cos(Kx-Wt)

Bo=2*10^-6 T

W=8.5*10^7 rad/sec

a)

E=E0*cos(Kx-Wt)

here

Eo=Bo*c

E=B0*cos(Kx-Wt)

here

speed of light c = 3*10^8 m/sec

b)

Eo=Bo*c

=2*10^-6*3*10^8

=6*10^2 V/m

=600 V/m

c)

W=2pi*f

or

f=w/2pi

or

f=8.5*10^7/2*3.14

=1.353*10^7 hz

d)

c=W/K

k=w/c

2pi/lambda=w/c

lambda=c*(2pi/w)

e)

lambda=c*(2pi/w)

=3*10^8*2*3.14/8.5*10^7

=22.164 m

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