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A plane electromagnetic wave has frequency 10¹⁴ Hz, travels in a medium of refractive index 1.4, propagates in the xy-plane making 30 deg with the x-axis, is polarized along z, and has an average Poynting-vector magnitude of 500 W/m². What is the approximate amplitude E0 of its electric field?

1. About 519 V/m
2. About 367 V/m
3. About 614 V/m
4. About 260 V/m

Correct answer: About 519 V/m

Solution

For a plane EM wave in a non-magnetic medium of index n, the average intensity is S = (1/2)*n*e0*c*E0² (the medium speed is c/n and the energy density scales with n). Solving, E0 = sqrt(2*S/(n*e0*c)) = sqrt(2*500/(1.4*8.85e-12*3e8)) = sqrt(1000/3.717e-3) = sqrt(2.69e5) approximately 519 V/m. The field is E = E0*cos(k*(x*cos30 + y*sin30) - wt) z-hat with w = 2*pi*10¹⁴ and k = n*w/c.

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