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A linearly polarized plane wave at 100 MHz is propagating in the $z$ direction. The electric field vector makes an angle of 30° with the $x$-axis. Its peaks amplitude is measured to be $2.0\:\mathrm{ V m}^{-1}$. Write down equations for the electric field and magnetic fields components of the wave as a function of distance, $z$, and time $t$, measured in meters and seconds respectively. Assume the phase term is zero.

Since the phase term is zero, I got that $E(z,t)=2\cos(kz-ωt)$. I think I should use $ω=2πf$ and $k=2πf/c$, but how can I split the electric field into $x$ and $y$ components? Also, I think $B(z,t)=E(z,t)/c$, so is the $x$ component of $B(z,t)$ equal to the $x$ component of $E(z,t)/c$? The $x$ component of the electric field at any time is $|E|\cos(30°)$ and the $y$ component of the electric field at any time is $|E|\sin(30°)$.

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  • $\begingroup$ You need to recognize that the $E$ and $B$ fields are vector quantities: $\vec{E}( z,t)$, $\vec{B}(z,t)$. $\endgroup$
    – Dave
    Mar 19, 2014 at 13:33
  • $\begingroup$ My answer is now posted below $\endgroup$ Mar 19, 2014 at 14:22

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The x component of E(z,t) is |E|cos(30)=2 V/m * (sqrt(3)/2) The y component of E(z,t) is |E|sin(30)=2 V/m * (1/2)

k=2πf/c = 2*pi/3 ω=2πf = 2*pi*10^8

E(z,t)=2(i(sqrt(3)/2)+j(1/2))cos(2*pi*z/3-2*pi*10^8*t) V/m B= (kxE)/c = (0i+0j+k)/(3E8) x (i(sqrt(3))+j) [cos(2*pi(z/3-10^8*t))] 10^(-8) T

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