1. An electromagnetic wave is represented by the magnetic field represented math

Question

1. An electromagnetic wave is represented by the magnetic field represented mathematically by

B = Bo sin [(6.591x10^8 s-1) t + (2.198 m-1) x]

(a) Find the frequency and wavelength of the wave
(b) Check that the speed of the wave is as expected, namely, c.
(c) What is the direction of motion of the wave?
(d) If the magnetic field is vibrating north-south, how is the electric field vibrating?
(e) If Bo = 4.000x10^-9 T, find Eo, the intensity of the electric field.
(f) Find the average intensity, S, of the wave.

Explanation / Answer

a)f=w/2pi =6.591*10^8/6.28 =1.036 *10^8 Hz (ans)

wavelength=2pi/k=6.28/2.198=2.857 m (ans)

b)speed,c=w/k =6.591*10^8/2.198 =2.998*10^8 m/sec (ans)

c) direction of motion =negative X direction

d)electric field vibrates perpendicular to B

EXB =C

so E X -j =-i

so E in -k direction that is negative Z direction

e)Eo =c*Bo =3*10^8 *4*10^-9 =1.2 N/C (ans)

f)average intensity =cBo^2/munot =3*10^8 *(4*10^-9)^2 /(4*3.14*10^-7)=3.82*10^-3 W/m^2 (ans)

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