PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 22:

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Presentation transcript:

PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 22: Comments on Mid-Term Exam Start reading Chap. 11 Equations in cgs (Gaussian) units Special theory of relativity Lorentz transformation relations 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Comments on Mid-Term Exam 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

F r E 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Recall from Lecture 4: Green’s function for 3-d Poisson equation in Cartesian coordinates: 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

03/24/2014 PHY 712 Spring 2014 -- Lecture 22

1 2 3 4 5 6 PHY 712 Spring 2014 -- Lecture 22 03/24/2014

1 2 3 4 5 6 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

1 2 3 4 5 6 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

1 2 3 4 5 6 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

1 2 3 4 5 6 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

1 2 3 4 5 6 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

03/24/2014 PHY 712 Spring 2014 -- Lecture 22

03/24/2014 PHY 712 Spring 2014 -- Lecture 22

03/24/2014 PHY 712 Spring 2014 -- Lecture 22

03/24/2014 PHY 712 Spring 2014 -- Lecture 22

03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Notions of special relativity The basic laws of physics are the same in all frames of reference (at rest or moving at constant velocity). The speed of light in vacuum c is the same in all frames of reference. y’ y v x x’ y’ x’ y x 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Lorentz transformations y’ y v x x’ y’ x’ y x 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Lorentz transformations -- continued 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Examples of other 4-vectors applicable to the Lorentz transformation: 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

The Doppler Effect 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

The Doppler Effect -- continued x y x’ v y’ k’ k 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Electromagnetic Doppler Effect (q=0) Sound Doppler Effect (q=0) 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Lorentz transformation of the velocity For an infinitesimal increment: 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Lorentz transformation of the velocity -- continued 03/24/2014 PHY 712 Spring 2014 -- Lecture 22

Example of velocity variation with b: ux/c uy/c 03/24/2014 PHY 712 Spring 2014 -- Lecture 22