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Ch 31: Electromagnetic Fields and Waves
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 31: Electromagnetic Fields and WavesProblem 50a
Chapter 31, Problem 50a

The intensity of sunlight reaching the earth is 1360 W/m2. Assuming all the sunlight is absorbed, what is the radiation-pressure force on the earth? Give your answer in newtons.

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Understand the concept: Radiation pressure is the pressure exerted by electromagnetic radiation on a surface. If all the sunlight is absorbed, the radiation pressure can be calculated using the formula: P = Ic, where I is the intensity of sunlight and c is the speed of light in a vacuum.
Calculate the radiation pressure: Substitute the given intensity of sunlight, I = 1360 W/m^2, and the speed of light, c = 3.00 × 10^8 m/s, into the formula for radiation pressure.
Determine the force due to radiation pressure: The force exerted by radiation pressure on the Earth can be calculated using the formula: F = P × A, where A is the cross-sectional area of the Earth that intercepts sunlight. The cross-sectional area of the Earth is given by A = πr^2, where r is the radius of the Earth.
Substitute the radius of the Earth: Use the Earth's radius, r = 6.37 × 10^6 m, to calculate the cross-sectional area A. Then, substitute this value and the previously calculated radiation pressure P into the formula for force.
Simplify the expression: Perform the necessary calculations to simplify the expression for the force F. This will give you the radiation-pressure force on the Earth in newtons.

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Key Concepts

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

Radiation Pressure

Radiation pressure is the force exerted by electromagnetic radiation on a surface. It arises from the momentum carried by photons, which can impart momentum when they are absorbed or reflected. The pressure can be calculated using the formula P = I/c, where P is the radiation pressure, I is the intensity of the radiation, and c is the speed of light in a vacuum.
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Intensity of Radiation

Intensity is defined as the power per unit area carried by a wave, in this case, sunlight. It is measured in watts per square meter (W/m²) and represents how much energy is delivered to a surface over a specific time. The intensity of sunlight reaching the Earth is approximately 1360 W/m², which is crucial for calculating the radiation pressure.
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Force Calculation

Force can be calculated using the relationship between pressure and area. The total force exerted by radiation pressure on an object can be found using the formula F = P × A, where F is the force, P is the radiation pressure, and A is the area over which the pressure is applied. In this context, the area would be the cross-sectional area of the Earth exposed to sunlight.
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Related Practice
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A laser beam shines straight up onto a flat, black foil of mass m. Find an expression for the laser power P needed to levitate the foil.

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At one instant, the electric and magnetic fields at one point of an electromagnetic wave are E=(200i^+300j^−50k^) V/m\(\mathbf{E}\) = (200 \(\hat{\mathbf{i}\)} + 300 \(\hat{\mathbf{j}\)} - 50 \(\hat{\mathbf{k}\)}) \(\text{ V/m}\) and B=B0(7.3i^−7.3j^+ak^ μT\(\mathbf{B}\)=B_0(7.3\(\hat{\mathbf{i}\)}-7.3\(\hat{\mathbf{j}\)}+a\(\hat{\mathbf{k}\)}\(\text{ }\]\mu\) T. What is the Poynting vector at this time and position?

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When the Voyager 2 spacecraft passed Neptune in 1989, it was 4.5×109 km from the earth. Its radio transmitter, with which it sent back data and s, broadcast with a mere 21 W of power. Assuming that the transmitter broadcast equally in all directions, What signal intensity was received on the earth?

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For a science project, you would like to horizontally suspend an 8.5 by 11 inch sheet of black paper in a vertical beam of light whose dimensions exactly match the paper. If the mass of the sheet is 1.0 g, what light intensity will you need?

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What is the total energy density in an electromagnetic wave of intensity 1000 W/m2?