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A plane electromagnetic wave is described by E_z = 100*cos(6e8 * t + 4*x) V/m as it travels through a medium. Determine the dielectric constant of that medium. (c = 3e8 m/s)

1. 1.5
2. 2.0
3. 2.4
4. 4.0

Correct answer: 4.0

Solution

From the wave, omega = 6e8 rad/s and k = 4 rad/m, so the phase speed v = omega/k = 6e8/4 = 1.5e8 m/s. For a nonmagnetic dielectric, v = c/sqrt(epsilon_r), giving epsilon_r = (c/v)² = (3e8/1.5e8)² = 2² = 4.

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