Ch. 31 - Maxwell's Equations and Electromagnetic Waves

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 31 - Maxwell's Equations and Electromagnetic Waves

Problem 39

Chapter 30, Problem 39

Suppose you have a car with a 100-hp engine. How large a solar panel would you need to replace the engine with solar power? Assume that the solar panels can utilize 20% of the maximum solar energy that reaches the Earth’s surface (1000 W/m²). Explain why or why not this is practical.

Verified step by step guidance

Step 1: Convert the car's engine power from horsepower to watts. Use the conversion factor: 1 horsepower (hp) = 746 watts. Multiply 100 hp by 746 W/hp to find the engine's power in watts.

Step 2: Determine the effective power output of the solar panels. Since the solar panels utilize 20% of the maximum solar energy reaching the Earth's surface, calculate the usable power per square meter by multiplying 1000 W/m² by 0.20.

Step 3: Calculate the total area of solar panels required to match the engine's power. Divide the engine's power (in watts) by the effective power output per square meter of solar panels obtained in Step 2.

Step 4: Assess the practicality of the solution. Consider factors such as the size of the solar panel area required, the availability of space on the car, and the efficiency of solar panels under varying conditions (e.g., weather, angle of sunlight).

Step 5: Conclude whether replacing the car's engine with solar panels is feasible based on the calculated area and practical considerations, such as the limitations of solar energy collection and storage for automotive use.

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Key Concepts

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

Horsepower and Power Conversion

Horsepower (hp) is a unit of power commonly used to measure the output of engines. One horsepower is equivalent to approximately 746 watts. To determine the power output of a 100-hp engine in watts, you would multiply 100 by 746, resulting in 74,600 watts. Understanding this conversion is essential for comparing the power needs of the car with the power generated by solar panels.

Solar Panel Efficiency

Solar panel efficiency refers to the percentage of sunlight that a solar panel can convert into usable electrical energy. In this scenario, the solar panels are assumed to have an efficiency of 20%, meaning they can convert 20% of the solar energy they receive into electricity. This efficiency is crucial for calculating how much solar panel area is needed to generate sufficient power to replace the car's engine.

Solar Energy Availability

Solar energy availability is the amount of solar power that reaches the Earth's surface, typically measured in watts per square meter (W/m²). In this case, the maximum solar energy available is given as 1000 W/m². To assess the practicality of using solar panels to power the car, one must consider both the available solar energy and the area required for the panels to generate the necessary power output.

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Textbook Question

Compare 1030 on the AM dial to 103.1 on FM. Which has the longer wavelength, and by what factor is it larger?

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Textbook Question

A satellite beams microwave radiation with a power of 16 kW toward the Earth’s surface, 550 km away. When the beam strikes Earth, its circular diameter is about 1500 m. Find the rms electric field strength of the beam.

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Textbook Question

(III) (a) When a circular parallel-plate capacitor is being charged as in Example 31–1, show that the Poynting vector $\vec{S}$ points radially inward toward the center of the capacitor, parallel to the plates.

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Textbook Question

(II) Laser light can be focused (at best) to a spot with a radius r equal to its wavelength ⋋. Suppose a 1.0-W beam of green laser light (⋋ = 5 x 10^-7 m) forms such a spot and illuminates a cylindrical object of radius r and length r (Fig. 31–25). Estimate (a) the radiation pressure and force on the object, and (b) its acceleration, if its density equals that of water and it absorbs all the radiation. [This order-of-magnitude calculation convinced researchers of the feasibility of “optical tweezers,” page 916.]

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Textbook Question

(a) When a circular parallel-plate capacitor is being charged as in Example 31–1, show that the Poynting vector $\vec{S}$ points radially inward toward the center of the capacitor, parallel to the plates.

(b) Integrate $\vec{S}$ over the cylindrical boundary of the capacitor gap to show that the rate at which energy enters the capacitor is equal to the rate at which electrostatic energy is being stored in the electric field of the capacitor (Section 24–4). Ignore fringing of $\vec{E}$ .

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Textbook Question

An amateur radio operator wishes to build a receiver that can tune a range from 14.0 MHz to 15.0 MHz. A variable capacitor has a minimum capacitance of 95 pF.

(a) What is the required value of the inductance?

(b) What is the maximum capacitance used on the variable capacitor?

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