Electromagnetic energy. First off, let's ask you guys a question. Do electromagnetic waves carry energy? Sure. How do you know that? What happens when you go outside and sit in the sunshine, especially like today? What happens when you absorb a lot of sunshine? You get warm, right? You get hot. That's because those electromagnetic waves, which are coming from the Sun, Travel all the way across space, punch through our atmosphere, come down, hit you. You're absorbing it. You are absorbing that energy. You get warm. Okay, so electromagnetic waves clearly carry energy. And we talked about this a little bit before with the idea of water, right? Water is H2O. It looks like that but it also has a dipole moment to it. And so, if we flip this thing to the right, and then flip it to the left, and flip it to the right, and flip it to the left. We can do that. And you'll get a little seasick. But if you do that at a particular frequency. 2.4 gigahertz. This thing turning right and left. That is of course your microwave oven. Okay, there's an electric field that's gonna do that. And so, we can draw this electric field coming in to do that. Now if that electromagnetic field is carrying energy, which it is. It's transferring it to the water and that's heating up your food. So there is some electric energy density. Which we talked about before. And the electric energy density was the following. Remember energy density is just energy per volume. And we ended up with one-half epsilon naught E squared. In the last chapter, we talked about the magnetic energy density. How much energy is in a magnetic field? And that was 1 over 2 mu naught B squared. So the total energy density in a wave is just going to be the sum of those two. It's one-half epsilon naught E squared plus 1 over 2 mu naught B squared. But the two components have equal contribution to the overall energy density. So we have the caveat that the electric interview density is, in fact, equal to the magnetic energy density. And so, we can write the total energy in that wave. U is what we're calling the energy density. And we can write it in terms of E. And if the electric part is equal to the magnetic part, we can just write it as twice the magnetic part. Epsilon naught E squared. Or we can write it in terms of the magnetic part. 1 over mu naught B squared. Okay, and this is what we're calling U. The total energy density. Okay so we have equal parts E and B. But let's take a look at this last equation here and see if we can determine the relationship between E and B. So what we said was one-half epsilon naught E squared is the same as 1 over 2 mu naught B squared. Let's multiply by 2 on each side get rid of the half. And now let's divide by an epsilon naught. And now let's take a square root of both sides. Okay, but we know what these values are. We know what epsilon naught is and mu naught is. So this becomes the following. E is 1 over the square root of epsilon naught, which we said was 8.85 times 10 to the minus 12. Mu naught was 4 pi times 10 to the minus 7. Can somebody punched this stuff into your calculator and tell me what you get, and I will approximate it here. And hopefully you got that. Anybody get that number? When they did 1 over the square root of all this stuff right here? That's right? So this is kind of cool, right? c, the speed of light, came about from that. You take those electric experiments that you did. And you figured out what epsilon was. You did some magnetic experiments and you figured out what mu naught was. And suddenly, you put them together in this special way and you get the speed of light. You get how fast electromagnetic waves travel across the universe. And this is the beauty of Maxwell's equations and Maxwell's derivation of this problem. Before Maxwell, nobody really knew definitively that light was electromagnetic waves. And it was only after Maxwell that we knew that.
Table of contents
- 0. Math Review31m
- 1. Intro to Physics Units1h 23m
- 2. 1D Motion / Kinematics3h 56m
- Vectors, Scalars, & Displacement13m
- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
- Calculating Change in Velocity from Acceleration-Time Graphs10m
- Graphing Position, Velocity, and Acceleration Graphs11m
- Kinematics Equations37m
- Vertical Motion and Free Fall19m
- Catch/Overtake Problems23m
- 3. Vectors2h 43m
- Review of Vectors vs. Scalars1m
- Introduction to Vectors7m
- Adding Vectors Graphically22m
- Vector Composition & Decomposition11m
- Adding Vectors by Components13m
- Trig Review24m
- Unit Vectors15m
- Introduction to Dot Product (Scalar Product)12m
- Calculating Dot Product Using Components12m
- Intro to Cross Product (Vector Product)23m
- Calculating Cross Product Using Components17m
- 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
- Uniform Circular Motion7m
- Period and Frequency in Uniform Circular Motion20m
- Centripetal Forces15m
- Vertical Centripetal Forces10m
- Flat Curves9m
- Banked Curves10m
- Newton's Law of Gravity30m
- Gravitational Forces in 2D25m
- Acceleration Due to Gravity13m
- Satellite Motion: Intro5m
- Satellite Motion: Speed & Period35m
- Geosynchronous Orbits15m
- Overview of Kepler's Laws5m
- Kepler's First Law11m
- Kepler's Third Law16m
- Kepler's Third Law for Elliptical Orbits15m
- Gravitational Potential Energy21m
- Gravitational Potential Energy for Systems of Masses17m
- Escape Velocity21m
- Energy of Circular Orbits23m
- Energy of Elliptical Orbits36m
- Black Holes16m
- Gravitational Force Inside the Earth13m
- Mass Distribution with Calculus45m
- 9. Work & Energy1h 59m
- 10. Conservation of Energy2h 54m
- Intro to Energy Types3m
- Gravitational Potential Energy10m
- Intro to Conservation of Energy32m
- Energy with Non-Conservative Forces20m
- Springs & Elastic Potential Energy19m
- Solving Projectile Motion Using Energy13m
- Motion Along Curved Paths4m
- Rollercoaster Problems13m
- Pendulum Problems13m
- Energy in Connected Objects (Systems)24m
- Force & Potential Energy18m
- 11. Momentum & Impulse3h 40m
- Intro to Momentum11m
- Intro to Impulse14m
- Impulse with Variable Forces12m
- Intro to Conservation of Momentum17m
- Push-Away Problems19m
- Types of Collisions4m
- Completely Inelastic Collisions28m
- Adding Mass to a Moving System8m
- Collisions & Motion (Momentum & Energy)26m
- Ballistic Pendulum14m
- Collisions with Springs13m
- Elastic Collisions24m
- How to Identify the Type of Collision9m
- Intro to Center of Mass15m
- 12. Rotational Kinematics2h 59m
- 13. Rotational Inertia & Energy7h 4m
- More Conservation of Energy Problems54m
- Conservation of Energy in Rolling Motion45m
- Parallel Axis Theorem13m
- Intro to Moment of Inertia28m
- Moment of Inertia via Integration18m
- Moment of Inertia of Systems23m
- Moment of Inertia & Mass Distribution10m
- Intro to Rotational Kinetic Energy16m
- Energy of Rolling Motion18m
- Types of Motion & Energy24m
- Conservation of Energy with Rotation35m
- Torque with Kinematic Equations56m
- Rotational Dynamics with Two Motions50m
- Rotational Dynamics of Rolling Motion27m
- 14. Torque & Rotational Dynamics2h 5m
- 15. Rotational Equilibrium3h 39m
- 16. Angular Momentum3h 6m
- Opening/Closing Arms on Rotating Stool18m
- Conservation of Angular Momentum46m
- Angular Momentum & Newton's Second Law10m
- Intro to Angular Collisions15m
- Jumping Into/Out of Moving Disc23m
- Spinning on String of Variable Length20m
- Angular Collisions with Linear Motion8m
- Intro to Angular Momentum15m
- Angular Momentum of a Point Mass21m
- Angular Momentum of Objects in Linear Motion7m
- 17. Periodic Motion2h 9m
- 18. Waves & Sound3h 40m
- Intro to Waves11m
- Velocity of Transverse Waves21m
- Velocity of Longitudinal Waves11m
- Wave Functions31m
- Phase Constant14m
- Average Power of Waves on Strings10m
- Wave Intensity19m
- Sound Intensity13m
- Wave Interference8m
- Superposition of Wave Functions3m
- Standing Waves30m
- Standing Wave Functions14m
- Standing Sound Waves12m
- Beats8m
- The Doppler Effect7m
- 19. Fluid Mechanics2h 27m
- 20. Heat and Temperature3h 7m
- Temperature16m
- Linear Thermal Expansion14m
- Volume Thermal Expansion14m
- Moles and Avogadro's Number14m
- Specific Heat & Temperature Changes12m
- Latent Heat & Phase Changes16m
- Intro to Calorimetry21m
- Calorimetry with Temperature and Phase Changes15m
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes9m
- Phase Diagrams, Triple Points and Critical Points6m
- Heat Transfer44m
- 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
- Magnetic Field Produced by Moving Charges10m
- Magnetic Field Produced by Straight Currents27m
- Magnetic Force Between Parallel Currents12m
- Magnetic Force Between Two Moving Charges9m
- Magnetic Field Produced by Loops and Solenoids42m
- Toroidal Solenoids aka Toroids12m
- Biot-Savart Law (Calculus)18m
- Ampere's Law (Calculus)17m
- 30. Induction and Inductance3h 37m
- 31. Alternating Current2h 37m
- Alternating Voltages and Currents18m
- RMS Current and Voltage9m
- Phasors20m
- Resistors in AC Circuits9m
- Phasors for Resistors7m
- Capacitors in AC Circuits16m
- Phasors for Capacitors8m
- Inductors in AC Circuits13m
- Phasors for Inductors7m
- Impedance in AC Circuits18m
- Series LRC Circuits11m
- Resonance in Series LRC Circuits10m
- Power in AC Circuits5m
- 32. Electromagnetic Waves2h 14m
- 33. Geometric Optics2h 57m
- 34. Wave Optics1h 15m
- 35. Special Relativity2h 10m
32. Electromagnetic Waves
Intensity of EM Waves
Video duration:
7mPlay a video:
Related Videos
Related Practice