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0. Math Review31m
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1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

35. Special Relativity

Inertial Reference Frames

Physics

35. Special Relativity

Inertial Reference Frames

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Problem 8

Textbook Question

In one experiment, 2000 photons are detected in a 0.10-mm-wide strip where the amplitude of the electromagnetic wave is 10 V/m. How many photons are detected in a nearby 0.10-mm-wide strip where the amplitude is 30 V/m?

Verified step by step guidance

Understand that the number of photons detected is proportional to the intensity of the electromagnetic wave, and the intensity is proportional to the square of the amplitude of the wave. This means $ I \propto A^2 $, where $ I $ is the intensity and $ A $ is the amplitude.

Write the relationship between the number of photons detected $ N $ and the amplitude $ A $: $ N \propto A^2 $. This implies $ \frac{N_2}{N_1} = \frac{A_2^2}{A_1^2} $, where $ N_1 $ and $ N_2 $ are the number of photons detected in the first and second strips, and $ A_1 $ and $ A_2 $ are their respective amplitudes.

Substitute the given values for $ A_1 $ and $ A_2 $: $ A_1 = 10 \, \text{V/m} $ and $ A_2 = 30 \, \text{V/m} $. The equation becomes $ \frac{N_2}{N_1} = \frac{(30)^2}{(10)^2} $.

Simplify the ratio: $ \frac{N_2}{N_1} = \frac{900}{100} = 9 $. This means the number of photons detected in the second strip is 9 times the number detected in the first strip.

Multiply the number of photons detected in the first strip by this ratio to find $ N_2 $: $ N_2 = 9 \times 2000 $. This gives the number of photons detected in the second strip.

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Key Concepts

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

Photon Detection

Photon detection refers to the process of identifying and counting individual photons, which are the fundamental particles of light. The number of detected photons can be influenced by factors such as the intensity of the light source and the area over which the detection occurs. In this context, the experiment measures how varying the amplitude of the electromagnetic wave affects the number of photons detected in a specified area.

Amplitude of Electromagnetic Waves

The amplitude of an electromagnetic wave is a measure of the maximum electric field strength of the wave. It is directly related to the intensity of the wave, which is proportional to the square of the amplitude. Higher amplitude indicates a stronger wave, which can lead to a greater number of photons being emitted or detected, as seen in the comparison between the two strips in the experiment.

Intensity and Photon Flux

Intensity in the context of electromagnetic waves is defined as the power per unit area and is proportional to the square of the amplitude. Photon flux, which is the number of photons passing through a unit area per unit time, increases with higher intensity. Therefore, by understanding the relationship between intensity, amplitude, and photon detection, one can calculate the expected number of photons detected in different conditions.

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