A transverse electromagnetic plane wave with a frequency of 2.13 MHz travels dir

Question

A transverse electromagnetic plane wave with a frequency of 2.13 MHz travels directly away from you (- z direction). At time t = 0, your magnetic field detector measures a magnetic field of 5.89 × 108 Tesla pointing down (- y direction) which further measurement reveals to be the maximum magentic field strength for the wave. Also at time t = 0 and at the location of your detector, what is the electric field associated with this wave? (Enter + if rigthward and - if leftward.)

1.77×101 N/C

B) At time t = 0, what is the electric field 32.9 meters directly behind (further away from you) your detector?

C) At time t = 4.61 × 107 seconds, what is the electric field at your detector?

D) At time t = 4.61 × 107 seconds, what is the electric field 37.1 centimeters directly to the right of your detector?

Explanation / Answer

Given that

frequency f=2.13MHz

magnetic field B=5.89*10^-8 T

now we find the electric field associated

the electric field E=Bc=5.89*10^-8*3*10^8=17.7 N/c

now we find the electric field at 32.9 meter

the electric field E=Eosin[w/c*x]

=17.7*sin[2*3.14*2.13*10^6*32.9/3*10^8]

=17.7*sin[1.5]

=0.46 N/c

now we find the electric field at t=4.61*10^-7 sec

the electric field E=17.7sin(2*3.14*2.13*10^6*4.61*10^-7]

=1.912 N/c

now we find the electric field at t=4.61*10^-7 and x=0.371 m

the electric field E=17.7*sin[2*3.14*2.13*10^6*4.61*10^-7-(2*3.14*2.13*10^6/3*10^8)*0.371]

=17.7*sin[6.2-0.017]

=1.91 N/c

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