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1. Intro to Physics Units1h 29m
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21. Kinetic Theory of Ideal Gases1h 50m
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30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

32. Electromagnetic Waves

Intro to Electromagnetic (EM) Waves

Physics

32. Electromagnetic Waves

Intro to Electromagnetic (EM) Waves

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3:57 minutes

Problem 38

Textbook Question

(II) What size should the solar panel on a satellite orbiting Jupiter be if it is to collect the same amount of radiation from the Sun as a 1.0-m² solar panel on a satellite orbiting Earth? [Hint: Assume the inverse square law.]

Verified step by step guidance

Understand the inverse square law: The intensity of radiation decreases with the square of the distance from the source. Mathematically, this is expressed as $ I \propto \frac{1}{r^2} $, where $ I $ is the intensity and $ r $ is the distance from the source.

Identify the given data: The solar panel on Earth has an area of 1.0 m² and collects a certain amount of solar radiation. The goal is to determine the area of the solar panel on Jupiter that collects the same amount of radiation.

Relate the intensities at Earth and Jupiter using the inverse square law: $ \frac{I_{Jupiter}}{I_{Earth}} = \frac{r_{Earth}^2}{r_{Jupiter}^2} $, where $ r_{Earth} $ is the distance from the Sun to Earth, and $ r_{Jupiter} $ is the distance from the Sun to Jupiter.

Express the relationship between the areas of the solar panels: Since the power collected by a solar panel is proportional to both the intensity of radiation and the area of the panel, we can write $ A_{Jupiter} \cdot I_{Jupiter} = A_{Earth} \cdot I_{Earth} $. Substituting $ I_{Jupiter} = I_{Earth} \cdot \frac{r_{Earth}^2}{r_{Jupiter}^2} $, we get $ A_{Jupiter} = A_{Earth} \cdot \frac{r_{Jupiter}^2}{r_{Earth}^2} $.

Substitute the known values: Use the distances $ r_{Earth} = 1 $ AU and $ r_{Jupiter} = 5.2 $ AU (astronomical units) to calculate $ A_{Jupiter} $. The final expression is $ A_{Jupiter} = 1.0 \cdot \frac{(5.2)^2}{(1.0)^2} $.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Inverse Square Law

The inverse square law states that the intensity of radiation from a point source decreases with the square of the distance from the source. In the context of solar radiation, this means that as a satellite moves further from the Sun, the amount of solar energy it receives per unit area diminishes significantly, requiring larger surface areas for solar panels to collect the same energy.

Solar Irradiance

Solar irradiance is the power per unit area received from the Sun, typically measured in watts per square meter (W/m²). At different distances from the Sun, the solar irradiance varies due to the inverse square law, affecting how much energy solar panels can collect. Understanding this concept is crucial for calculating the necessary size of solar panels on satellites at varying distances.

Area of Solar Panels

The area of solar panels directly influences their ability to capture solar energy. To maintain the same energy collection as a smaller panel at a closer distance, a larger panel is required at a greater distance. This relationship is essential for determining the appropriate size of solar panels on satellites orbiting different celestial bodies, such as Earth and Jupiter.

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(II) Pulsed lasers used for science and medicine produce very brief bursts of electromagnetic energy. If the laser light wavelength is 1062 mm (Neodymium–YAG laser), and the pulse lasts for 32 picoseconds, how many wavelengths are found within the laser pulse? How brief would the pulse need to be to fit only one wavelength?

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(II) What size should the solar panel on a satellite orbiting Jupiter be if it is to collect the same amount of radiation from the Sun as a 1.0-m2 solar panel on a satellite orbiting Earth? [Hint: Assume the inverse square law.]

Key Concepts

Inverse Square Law

Solar Irradiance

Area of Solar Panels

Watch next

(II) What size should the solar panel on a satellite orbiting Jupiter be if it is to collect the same amount of radiation from the Sun as a 1.0-m² solar panel on a satellite orbiting Earth? [Hint: Assume the inverse square law.]