Module 3 : MAGNETIC FIELD
Lecture 20 : Magnetism in Matter
  Example 26 :
  The electric field of a plane electromagnetic wave in vacuum is $ E_y = 0.5\cos[2\pi\times 10^8(t-x/c)]$ V/m, $E_x=E_z=0$. Determine the state of polarization and the direction of propagation of the wave. Determine the magnetic field.
  Solution :
Comparing with the standard form for a harmonic wave
 
  so that $\lambda = c/10^8 = 3$ m. the direction of propagation is x-direction. Since the electric field oscillates in x-y plane, this is the plane of polarization. Since $\vec B$ must be perpendicular to both the electric field direction and the direction of propagation, $\vec B$ has only z-component with an amplitude $B_0=E_0/c\simeq 1.66\times 10^{-9}$ T. Thus
 
\begin{displaymath}B_z = 1.66\times 10^{-9}\cos[2\pi\times 10^8(t-x/c)]\ \ {\rm T}\end{displaymath}

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