/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 The sun delivers \(10^{4} \mathr... [FREE SOLUTION] | 91Ó°ÊÓ

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The sun delivers \(10^{4} \mathrm{Wm}^{-2}\) of electromagnetic flux to the earth's surface. The total power that in incident on a roof of dimensions \(10 \mathrm{~m}^{2}\) will be (a) \(10^{4} \mathrm{~W}\) (b) \(10^{5} \mathrm{~W}\) (c) \(10^{6} \mathrm{w}\) (d) \(10^{7} \mathrm{~W}\)

Short Answer

Expert verified
The answer is (b) \(10^{5} \, \mathrm{W}\).

Step by step solution

01

Understand the Problem

We need to calculate the total power incident on a roof given the flux of electromagnetic energy from the sun and the area of the roof.
02

Recall the Formula for Power

The power incident on an area by electromagnetic flux is given by the formula: \( P = F \times A \) where \( P \) is the power, \( F \) is the flux, and \( A \) is the area.
03

Apply Given Values

We know that the flux \( F = 10^{4} \, \mathrm{Wm}^{-2} \) and the area \( A = 10 \, \mathrm{m}^{2} \). Plug these values into the formula: \( P = 10^{4} \, \mathrm{Wm}^{-2} \times 10 \, \mathrm{m}^{2} \).
04

Calculate Power

Calculate the power: \( P = 10^{4} \times 10 = 10^{5} \, \mathrm{W} \).
05

Match the Value with Options

Review the options given in the problem: (a) \(10^{4} \, \mathrm{W}\), (b) \(10^{5} \, \mathrm{W} \), (c) \(10^{6} \, \mathrm{W}\), (d) \(10^{7} \, \mathrm{W}\). The calculated power, \(10^{5} \, \mathrm{W}\), corresponds to option (b).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solar Power Calculation
Calculating solar power is essential for optimizing the use of solar energy installations. The sun delivers electromagnetic flux to the Earth's surface. This flux is a measure of how much solar energy reaches a specific area. In the original exercise, this was given as \(10^{4} \mathrm{Wm}^{-2}\). To find out how much power hits a certain area, like a rooftop solar panel, you use a simple formula: \( P = F \times A \).
Here, \(P\) represents the power in watts, \(F\) is the flux, and \(A\) is the area in square meters. For example, if the electromagnetic flux is \(10^{4} \mathrm{Wm}^{-2}\) and the roof area is \(10 \mathrm{~m}^{2}\), you calculate the power as follows:
  • Find the product of flux and area: \(10^{4} \times 10 = 10^{5} \, \mathrm{W}\)
  • The result, \(10^{5} \, \mathrm{W}\), represents the total solar power incident on the roof.
By understanding how to use this simple calculation, you can effectively determine the potential solar power you can harness from different surfaces.
Electromagnetic Energy
Electromagnetic energy from the sun is a potent and renewable energy source. It travels to Earth as electromagnetic waves, encompassing a wide spectrum that includes visible light, UV, and infrared radiation. This energy is incident on surfaces like the roof in the exercise.
Key aspects of electromagnetic energy include:
  • Its capability to travel through a vacuum, meaning solar power can be harnessed on even cloudy days, although the efficiency might vary.
  • The speed at which it travels—reaching Earth in about 8 minutes from the sun.
Understanding electromagnetic energy is crucial for fields like solar energy management and physics. It allows for the conversion of natural sunlight into practical electricity through photovoltaic systems. With its broad applications, studying this energy form enables breakthroughs in sustainable energy solutions and supports wider adoption of green technologies.
Physics Problem Solving
Solving physics problems is about applying concepts and formulas to real-world scenarios. Every physics problem-solving process follows certain logical steps. Let's break down the approach as seen in the original exercise.
Begin with understanding the problem. Identify what is given and what needs to be found. In the exercise, the metric to calculate was the total power incident on the roof.Next, use the right formula. In this case, \( P = F \times A \) was used to connect flux and area to the total power.
  • Recognize key variables and their units. It's critical to ensure that units match so calculations are accurate.
  • Substitute the values into the equation. This provides a clear path to the solution.
Finally, interpret the result. Compare it with the given options to confirm the accuracy. Problem-solving involves a step-by-step logical approach, reinforced by checking calculations and rationalizing the outcome. Mastering this process not only helps in exercises but also in tackling novel real-world challenges.

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Most popular questions from this chapter

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A plane electromagnetic wave is incident on a material surface. The wave delivers momentum \(p\) and energy, \(E\). (a) \(p \neq 0, E \neq 0\) (b) \(p=0, E=0\) (c) \(p=0, E \neq 0\) (d) \(p \neq 0, E=0\)

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