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?

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 = B_{o 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 = E_o sin(kx ± ωt )

 E_z =(8×10⁶ )× (3×10⁸) sin(2×10¹¹ t + 300∏X ) ..........(3)

 

Equestion (3) gives the expression for electric field.