The oscillating magnetic field in a plane EM waves is given by By=8x10to the power of 6sin[2x10to the power of 11 t+300pie x]T.Calculate wavelength of EM wave and also write an expression for oscillatin electric field?

Asked by SUHAS MELMURI | 14th Nov, 2013, 05:38: AM

Expert Answer:

Given that,
B = 8×106 sin(2×1011 t + 300∏X ) T     .....................(1)
 
Now the standard equestion of magnetic field is always written in the form of
 
B = Bo sin(kx ± ωt ) T                                         ...........................(2)
 
      Where, Bo = amplitude of EM wave
                  k = wave vector
                  ω = frequency of osscilation
 
By comparing eq (1) with (2),
    k = 300∏
 
The wave vector is given by,
    k = 2∏/λ
 
    λ = 2∏/k
       = 2∏/300∏
       = 0.0066 m
       = 6.6 × 10-3 m
 
In a plane EM wave direction of magnetic field, electric field and direction of propagation are always mutualy perpendicular to each other.
 
Therefore, from eq (1) the electric field is in Z - direction.
 
The relation between electric and magnetic field is given by,
 
Hence,
 E = Eo sin(kx ± ωt )
 Ez =(8×106 )× (3×108) sin(2×1011 t + 300∏X ) ..........(3)
 
Equestion (3) gives the expression for electric field.

Answered by Komal Parmar | 18th Nov, 2013, 04:41: PM

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