The electric field of an E/M wave is described by: $$\mathbf{E} = E_0\sin\left(kx-\omega t\right)\hat{\mathbf{y}}$$ What is the direction of the magnetic field? 1. $+x$ 2. $+y$ 3. $–x$ 4. $+z$ 5. $-z$ Note: * Correct Answer: D

You have this solution to Maxwell's equations in vacuum: $$\widetilde{\mathbf{E}}(x,y,z,t) = \widetilde{\mathbf{E}}_0 \exp\left[i\left(\mathbf{k}\cdot\mathbf{r} - \omega t\right)\right]$$ If this wave travels in the $y$ direction, is polarized in the $x$ direction, and has a complex phase of 0, what is the $x$ component of the physical wave? 1. $E_x = E_0 \ cos\left(kx-\omega t\right)$ 2. $E_x = E_0 \ cos\left(ky-\omega t\right)$ 3. $E_x = E_0 \ cos\left(kz-\omega t\right)$ 4. $E_x = E_0 \ cos\left(k_x x+k_y y-\omega t\right)$ 5. Something else Note: * Correct Answer: B

An electromagnetic plane wave propagates to the right. Four vertical antennas are labeled 1-4. 1, 2, and 3 lie in the $x-y$ plane. 1, 2, and 4 have the same $x$-coordinate, but antenna 4 is located further out in the $z$-direction. Rank the time-averaged signals received by each antenna. <img src="./images/EM_waves_antenna.png" align="right" style="width: 700px";/> 1. 1=2=3$>$4 2. 3$>$2$>$1=4 3. 1=2=4$>$3 4. 1=2=3=4 5. 3$>$1=2=4 Note: * Correct Answer: D

A point source of radiation emits power $P_0$ isotropically (uniformly in all directions). A detector of area $a_d$ is located a distance $R$ away from the source. What is the power $P_d$ received by the detector? <img src="./images/detector_spherical.png" align="right" style="width: 300px";/> 1. $\frac{P_0}{4\pi R^2}a_d$ 2. $P_0\frac{a_d^2}{R^2}$ 3. $P_0\frac{a_d}{R}$ 4. $\frac{P_0}{\pi R^2}a_d$ 5. None of these Note: * Correct Answer: A