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Electromagnetic fields and waves 2

# Electromagnetic fields and waves 2 - Physics 113...

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Physics 102: Lecture 15, Slide 1 Physics 113 Electricity and Magnetism Lecture 17: Electromagnetic Fields and Waves (Knight: 34.1 to 34.5) Physics 113 Dr. Renat Letfullin

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Physics 102: Lecture 15, Slide 2 Electromagnetic Waves
Physics 102: Lecture 15, Slide 3 Maxwell’s Equations in 0 / E dA Q ε = r r Ñ 0 B dA = r r Ñ m d E ds dt Φ = - r r Ñ 0 through 0 0 e d B ds I dt μ μ ε Φ = + r r Ñ Gauss’s Law Gauss’s Law for magnetism Faraday’s Law Ampère-Maxwell Law ( ) F q E v B = + × r r r r Lorentz Force Law (magnetic monopole charge goes here) (magnetic monopole current goes here) Physics 113 Dr. Renat Letfullin

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Physics 102: Lecture 15, Slide 4 Electromagnetic Waves Maxwell’s formulation of electricity and magnetism has an interesting consequence. The equations can be manipulated to give a wave equations for E and B of the form: 2 2 0 0 2 2 d E d E dx dt μ ε = This can be recognized as describing an electromagnetic wave traveling through space with a velocity of: EM wave 0 0 9 2 2 7 2 8 1 (4 9.0 10 Nm /C ) (4 10 N/A ) 3.0 10 m/s v μ ε π π - = × × = × = × Physics 113 Dr. Renat Letfullin
Physics 102: Lecture 15, Slide 5 Propagation of EM Waves Changing B field creates E field Changing E field creates B field E = c B x z y If you decrease E, you also decrease B! This is important ! Physics 113 Dr. Renat Letfullin

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Physics 102: Lecture 15, Slide 6 x z y E B loop in xy plane loop in xz plane loop in yz plane 1 2 3 Which orientation will have the largest induced emf? Hint: Look at flux of B. Concept question Physics 113 Dr. Renat Letfullin
x z y E B Only the loop in the xy plane will have a magnetic flux through it as the wave passes. The flux will oscillate with time and induce an emf. (Faraday’s Law!) loop in xy plane loop in xz plane loop in yz plane 1 2 3 Which orientation will have the largest induced emf? Concept question

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Physics 102: Lecture 15, Slide 8 Energy of Electromagnetic Waves and Polarization Physics 113 Dr. Renat Letfullin
Physics 102: Lecture 15, Slide 9 Electric Fields Recall Capacitor Energy: U = ½ C V 2 Average Energy Density: u E = ½ (½ ε 0 E 0 2 ) = ½ ε 0 E 2 rms Energy in EM wave Light waves carry energy but how much?

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