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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
Chapter 31, Problem 23a

FIGURE EX31.23 shows a horizontally polarized radio wave of frequency 1.0×106 Hz traveling into the figure. The maximum electric field strength is 1000 V/m. What is the maximum magnetic field strength?

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Step 1: Recall the relationship between the electric field strength (E) and the magnetic field strength (B) in an electromagnetic wave. The two are related by the speed of light (c), where c = E / B.
Step 2: Use the known value of the speed of light, c = 3.0 × 10^8 m/s, to relate the maximum electric field strength to the maximum magnetic field strength.
Step 3: Substitute the given maximum electric field strength, E = 1000 V/m, into the formula B = E / c.
Step 4: Perform the division to find the maximum magnetic field strength, B. Ensure the units are consistent (V/m for E and m/s for c).
Step 5: Interpret the result to understand the physical meaning of the maximum magnetic field strength in the context of the electromagnetic wave shown in the figure.

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Key Concepts

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

Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space. They consist of perpendicular electric (E) and magnetic (B) fields, which oscillate in phase and are oriented at right angles to each other and the direction of wave propagation. The speed of these waves in a vacuum is the speed of light, approximately 3.00 × 10^8 m/s.
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Maxwell's Equations

Maxwell's Equations describe how electric and magnetic fields interact and propagate. They establish that a changing electric field generates a magnetic field and vice versa. These equations are fundamental to understanding electromagnetic waves, as they explain the relationship between the electric field strength and the magnetic field strength in a propagating wave.
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Relationship Between Electric and Magnetic Fields

In an electromagnetic wave, the maximum magnetic field strength (B_max) is related to the maximum electric field strength (E_max) by the equation B_max = E_max/c, where c is the speed of light. This relationship shows that the magnetic field strength is directly proportional to the electric field strength, allowing for the calculation of one field if the other is known.
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