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The intensity of an electromagnetic wave from a source is (500/pi) W/m². Find the amplitude of the electric field in this wave.

1. sqrt(3) * 10² N/C
2. 2*sqrt(3) * 10² N/C
3. (sqrt(3)/2) * 10² N/C
4. 2*sqrt(3) * 10¹ N/C

Correct answer: 2*sqrt(3) * 10² N/C

Solution

The time-averaged intensity of an EM wave is I = (1/2)*epsilon0*c*E0². Substituting I = 500/pi, we can solve for E0. I = 500/pi ~ 159.15 W/m². E0² = 2I/(epsilon0*c) = 2*(500/pi)/(8.85e-12 * 3e8) = (1000/pi)/(2.655e-3) = 1000/(pi*2.655e-3) = 1000/8.341e-3 = 119,890 ~ 1.2e5. E0 = sqrt(1.2e5) ~ 346 N/C ~ 2*sqrt(3)*100 = 346 N/C. So answer is 2*sqrt(3)*10² N/C.

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