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The magnetic field \(H\) (in A/m) of a plane wave propagating in free space is given by \[ \mathbf{H}=\hat{x}\left(\frac{5\sqrt{3}}{\eta_0}\right)\cos(\omega t-\beta z)+\hat{y}\left(\frac{5}{\eta_0}\right)\sin(\omega t-\beta z+\pi/2). \] The time-average power flow density in W/m² is

1. η0/100
2. 100/η0
3. 50η0²
4. 50/η0

Correct answer: 50/η0

Solution

The given components are in quadrature and represent a circularly polarized plane wave. The magnetic-field magnitude is constant: \(H_0=\sqrt{(5\sqrt3/\eta_0)^2+(5/\eta_0)^2}=10/\eta_0\). Hence the average power density is \(\langle S\rangle=\eta_0 H_0^2/2=50/\eta_0\).

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