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Chapter 31: Problem 59

As shown in the figure, sunlight is coming straight down (negative \(z\) -direction) on a solar panel (of length \(L=1.40 \mathrm{~m}\) and width \(W=0.900 \mathrm{~m}\) ) on the Mars rover Spir- it. The amplitude of the electric field in the solar radiation is \(673 \mathrm{~V} / \mathrm{m}\) and is uniform (the radiation has the same amplitude everywhere). If the solar panel has an efficiency of \(18.0 \%\) in converting solar radiation into electrical power, how much average power can the panel generate?

Short Answer

Expert verified
Solution: After performing the calculations, the average power generated by the solar panel is: \(P = \left(\frac{1}{2} \cdot 8.85 \times 10^{-12} \, \text{F/m} \cdot 3.00 \times 10^8 \, \text{m/s} \cdot (673 \, \text{V/m})^2 \right) \cdot 0.180 \cdot (1.40\,\text{m} \cdot 0.900\,\text{m})\) Calculate the value of \(P\), and provide the result in watts.

Step by step solution

01

Calculate the intensity of solar radiation

Using the given amplitude of the electric field, \(E = 673 \,\text{V/m}\), we can calculate the intensity of the solar radiation using the formula: \(I = \frac{1}{2} \epsilon_0 c E^2\), where \(\epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m}\) is the permittivity of free space, and \(c = 3.00 \times 10^8 \, \text{m/s}\) is the speed of light. \(I = \frac{1}{2} \cdot 8.85 \times 10^{-12} \, \text{F/m} \cdot 3.00 \times 10^8 \, \text{m/s} \cdot (673 \, \text{V/m})^2\)
02

Calculate the active surface area of the solar panel

Given the dimensions of the solar panel, we can find the active surface area by multiplying its length and width: \(A = L \cdot W = 1.40\,\text{m} \cdot 0.900\,\text{m}\)
03

Calculate the average power generated by the solar panel

To find the average power generated, we have to multiply the intensity of solar radiation, the efficiency of the solar panel, and the active surface area: \(P = I \cdot \eta \cdot A\), where \(\eta = 18.0\% = 0.180\) \(P = \left(\frac{1}{2} \cdot 8.85 \times 10^{-12} \, \text{F/m} \cdot 3.00 \times 10^8 \, \text{m/s} \cdot (673 \, \text{V/m})^2 \right) \cdot 0.180 \cdot (1.40\,\text{m} \cdot 0.900\,\text{m})\) Now, calculate the value of \(P\) to get the average power generated by the solar panel.

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