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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 42b
Chapter 31, Problem 42b

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

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Understand the relationship between the intensity \( I \) of an electromagnetic wave and its energy density \( u \). The formula is \( I = c \cdot u \), where \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \; \text{m/s} \)).
Rearrange the formula to solve for the energy density \( u \): \( u = \frac{I}{c} \).
Substitute the given intensity \( I = 1000 \; \text{W/m}^2 \) into the formula: \( u = \frac{1000}{c} \).
Use the value of \( c = 3 \times 10^8 \; \text{m/s} \) to rewrite the equation: \( u = \frac{1000}{3 \times 10^8} \).
Simplify the expression to find the energy density \( u \). This will give you the total energy density in \( \text{J/m}^3 \).

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Key Concepts

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

Energy Density in Electromagnetic Waves

Energy density in electromagnetic waves refers to the amount of energy stored in a given volume of space. It is typically expressed in joules per cubic meter (J/m³) and is a crucial concept for understanding how energy propagates through electromagnetic fields, such as light.
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Intensity of Electromagnetic Waves

Intensity is defined as the power per unit area carried by an electromagnetic wave, measured in watts per square meter (W/m²). It quantifies how much energy is transmitted through a surface perpendicular to the direction of the wave's propagation, and is directly related to the energy density of the wave.
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Relationship Between Intensity and Energy Density

The relationship between intensity (I) and energy density (u) in an electromagnetic wave is given by the equation I = (1/2) * c * u, where c is the speed of light in a vacuum. This relationship allows us to calculate the total energy density from the intensity of the wave, providing a direct link between these two important concepts.
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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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Textbook Question

At one instant, the electric and magnetic fields at one point of an electromagnetic wave are E→=(200i^+300j^−50k^) V/m\(\overrightarrow{E}\)=(200\(\hat{i}\)+300\(\hat{j}\)-50\(\hat{k}\))\(\text{ V/m}\) and B→=B0(7.3i^−7.3j^+ak^) μT\(\overrightarrow{B}\)=B_0(7.3\(\hat{i}\)-7.3\(\hat{j}\)+a\(\hat{k}\))\(\text{ }\[\mu\]\text{T}\). What are the values of aa and B0B_0?

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