Classical Mechanics and Electromagnetism Overview
Delve into the intricacies of classical mechanics and electromagnetism through detailed discussions on topics such as plane waves, Lienard-Wiechert potentials, Maxwell's equations, Poynting vector, and retarded time. Explore the fundamental principles and concepts that govern the behavior of electromagnetic fields in a vacuum, as well as the relativistic aspects of Lienard-Wiechert potentials. Gain insights into the propagation of electromagnetic information and the impact of retarded time on field interactions.
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Presentation Transcript
1 1 Plane Waves & Lienard Wierchert Potential Jeffrey Eldred Classical Mechanics and Electromagnetism June 2018 USPAS at MSU
2 2 Plane Waves 2 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Maxwells Equations in a Vacuum d'Alembertian: Full solution is a plane wave: E1 and E2 are complex, the relative phase determines the polarization. 3 3 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Poynting Vector The E & B field are oriented normal to the direction of propagation: The Poynting vector describes the energy flow per unit area of the fields: And the time average of the Poynting vector for a plane wave: If E and H are complex, the time average can be written simply: 4 4 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
5 5 Lienard Wierchert Potentials: Relativistic 5 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Fields at the Speed of Light The plane wave illustrates the speed at which electromagnetic information is propagated. The fields from a moving charge radiate outward at speed c. See Java Demo. 6 6 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Retarded Time A point in space is affected by the E-fields originating from a source in the past, at a time called the retarded time. In the past, the position of the source will have changed and that will in turn impact the time that should be evaluated. 7 7 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Retarded Time & Light Cone 8 8 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Potentials for Retarded Time 9 9 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
10 10 Moving Point Charge 10 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Moving Point Charge Solve by change of variables: 11 11 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Moving Point Charge 12 12 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Moving Point Charge Potentials We have derived: A similar derivation shows that: 13 13 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Alternate Derivation With some algebra, it can be shown: 14 14 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Lienard-Wierchert Potentials By using the instantaneous velocity of the particle at tret, the expression we derived can be applied to any particle movement, not just straight line movement. 15 15 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Fields from a Point Charge 16 16 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Power Radiated from Accelerating Charge Radiation in reference frame in which Beta is small: Integrate over Poynting for radiation: 17 17 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
Power Radiated from Accelerating Charge Total power radiated: Linear acceleration: Circular acceleration: Can also be written 18 18 2/22/2025 Classical Mechanics and Electromagnetism | June 2018 USPAS at MSU
