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0. Math Review31m
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1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
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5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
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10. Conservation of Energy2h 54m
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14. Torque & Rotational Dynamics2h 5m
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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
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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

32. Electromagnetic Waves

Intro to Electromagnetic (EM) Waves

Physics

32. Electromagnetic Waves

Intro to Electromagnetic (EM) Waves

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3:32 minutes

Problem 19

Textbook Question

(II) Our nearest star (other than the Sun) is 4.2 light-years away. That is, it takes 4.2 years for the light it emits to reach Earth. How far away is it in meters?

Verified step by step guidance

Understand the problem: The distance to the star is given in light-years, which is the distance light travels in one year. To convert this to meters, we need to calculate how far light travels in one year and then multiply by 4.2.

Recall the speed of light: The speed of light in a vacuum is approximately $ c = 3.00 \times 10^8 \; \text{m/s} $.

Calculate the number of seconds in one year: Use the fact that there are 365.25 days in a year (accounting for leap years), 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Multiply these values to find the total seconds in a year: $ t = 365.25 \times 24 \times 60 \times 60 \; \text{s} $.

Determine the distance light travels in one year: Multiply the speed of light $ c $ by the total seconds in a year $ t $ to find the distance light travels in one year: $ d_{\text{1 year}} = c \times t $.

Calculate the total distance to the star: Multiply the distance light travels in one year $ d_{\text{1 year}} $ by 4.2 to find the total distance in meters: $ d_{\text{star}} = 4.2 \times d_{\text{1 year}} $.

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Key Concepts

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

Light-Year

A light-year is a unit of distance that represents how far light travels in one year in a vacuum. Since light moves at approximately 299,792 kilometers per second, a light-year is equivalent to about 9.46 trillion kilometers or about 5.88 trillion miles. This concept is essential for converting astronomical distances into more familiar units.

Distance Conversion

Distance conversion involves changing a measurement from one unit to another, such as from light-years to meters. To convert light-years to meters, one must multiply the number of light-years by the number of meters in a light-year, which is approximately 9.461 x 10^15 meters. Understanding this process is crucial for accurately determining distances in space.

Astronomical Units

Astronomical units (AU) are a standard unit of measurement used in astronomy to describe distances within our solar system. One AU is the average distance from the Earth to the Sun, approximately 149.6 million kilometers. While the question specifically asks for a conversion to meters, familiarity with AU helps contextualize distances in space and their relative scales.

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(II) A light-year is a measure of distance (not time). How many meters does light travel in a year?

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(II) An electromagnetic wave has an electric field given by $\vec{E} = \hat{i} (2775 V/m) \sin [(0.053 m^{- 1}) z - (1.6 \times 10^{7} rad/s) t]$ .