Chapt37_VG - Chapter 37. Relativity Chapter 1. Newtons laws...

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Chapter 37. Relativity Chapter 37. Relativity 1. Newton’s laws and Maxwell’s equations describe the motion of charged particles and the propagation of electromagnetic waves under circumstances where the Quantum effects we discussed last week can be ignored. 2. There are some inconsistencies when the speed of motion of objects or observers approaches the speed of light. 3. These inconsistencies are resolved by Einstein’s Special Theory of relativity The General theory describes gravitation and accelerating observers. The Special theory addresses modifications of Newton’s Laws and relations between measurements made by different observers
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Classical Physics ! E d ! A " = Q in ε 0 ! B d ! A " = 0 ! B ( ! r ) d ! s = " μ 0 ( I through + 0 d dt ! E d ! A ) surface loop ! E d ! S " = d dt ! B d ! A Surface Maxwell’s Equations m d dt ! v i = q ! E + ! v i × ! B ( ) d dt ! x i = ! v i Q in = q i i I through ! L = q i i ! v i Newton’s Laws E, B Q in , I thr Describes EM waves Describes motion of particles
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Special Relativity: Two components 1. How are the laws of physics modified when objects move close to the speed of light? 2. What do observers who are moving relative to each other measure when something happens? How are the measurements related? You will be surprised to learn that very little changes in terms of the mathematical statement of the laws of physics. You will be puzzled by the counterintuitive relations between measurements made by moving observers. Most of the conceptual difficulty is here.
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Maxwell’s Equations describe the excitation of electromagnetic fields by moving charges. If charges’ positions and velocities are known MEs tell us what are the electromagnetic fields, including the generation and propagation of light waves. ! E d ! A " = Q in ε 0 ! B d ! A " = 0 ! B ( ! r ) d ! s = " μ 0 ( I through + 0 d dt ! E d ! A ) surface loop ! E d ! S " = d dt ! B d ! A Surface How many, and which ones need to be modified? 1. All 2. Some - first two 3. Some - second two 4. None 5. None of the above
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Newton’s Laws with the Lorenz force tells us how charged particles move in electromagnetic fields. d dt ! p i = q ! E + ! v i × ! B ( ) d dt ! x i = ! v i Newton’s Laws ! p i = m ! v i How many, and which ones need to be modified? 1. All 2. #1 3. #2 4. #3 5. None 6. None of the above #1 #2 #3 ! p i = m γ i ! v i #2’ i = 1/ 1 ! v i 2 / c 2 Momentum can become large, but particle speed is always less than c
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Reference Frames: Two observers moving relative to each other measure different values for some quantities. S S’ Observer stationary in S Observer stationary in S’ y y’ x x’ v Reference frame S’ is moving at velocity v in the x direction with respect to Reference frame S. Reference frame S is
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Chapt37_VG - Chapter 37. Relativity Chapter 1. Newtons laws...

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