Sunlight is coming straight down on a solar panel (length 1.25 m and width W=0.850 m)belonging to the Spirit Mars rover.The amplitude of the electric field in the solar radiation is 642 V/m and is uniform (the radiation has the same amplitude everywhere).If the solar panel has an efficiency of 20.4 percent in converting solar radiation into electrical power,how much average power can the panel generate from the solar radiation?

Question

Quizplus · Accepted Answer

The average power $P_{\text{avg}}$ absorbed by the solar panel can be calculated using the formula for the intensity $I$ of the electromagnetic wave, which is given by $I = \frac{1}{2} c \epsilon_0 E^2$, where $c$ is the speed of light in vacuum ($3.00 \times 10^8$ m/s), $\epsilon_0$ is the permittivity of free space ($8.85 \times 10^{-12}$ C$^2$/N$\cdot$m$^2$), and $E$ is the amplitude of the electric field (642 V/m). The area $A$ of the solar panel is $1.25 \times 0.850$ m$^2$. The power absorbed by the panel is $P_{\text{abs}} = I \times A$, and the average power generated $P_{\text{avg}}$ is this absorbed power multiplied by the efficiency ($20.4\%$).First, calculate the intensity $I$:$$I = \frac{1}{2} \times 3.00 \times 10^8 \times 8.85 \times 10^{-12} \times (642)^2 \approx 548.3 \, \text{W/m}^2$$Then, calculate the area $A$:$$A = 1.25 \times 0.850 = 1.0625 \, \text{m}^2$$Next, calculate the power absorbed $P_{\text{abs}}$:$$P_{\text{abs}} = I \times A \approx 548.3 \times 1.0625 \approx 582.8 \, \text{W}$$Finally, calculate the average power generated $P_{\text{avg}}$:$$P_{\text{avg}} = P_{\text{abs}} \times 20.4\% \approx 582.8 \times 0.204 \approx 118.9 \, \text{W}$$Therefore, the correct answer is approximately 119 W.

Sunlight Is Coming Straight Down on a Solar Panel (Length