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Lecture21_Kim

# Lecture21_Kim - Lecture 21-1 PHYS241 Question 1 November 8...

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Lecture 21-1 PHYS241 – Question 1 – November 8, 2011 To you, the Exam II was a. Much more difficult than expected b. More difficult than expected c. About as expected d. Easier than expected e. Much easier than expected

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Lecture 21-2 PHYS241 – Question 2 – November 8, 2011 On the Exam II, you think you did a. Very well b. Well c. Average d. Poorly e. Very poorly
Lecture 21-3 Maxwell’s Equations (so far) Gauss’s law 0 inside S Q E d A  Gauss’ law for magnetism 0 S B d A Faraday’s law B C d E dl dt    Ampere’s law 0 C B dl I

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Lecture 21-4 We have seen that a changing magnetic field induces an electric field Faraday’s Law of Induction : In a similar manner, a changing electric field induces a magnetic field Maxwell’s Law of Induction : where B is the magnetic field induced in a closed loop by a changing electric flux E in that loop as shown below B d E dl dt   00 E d B dl dt   We charge the capacitor and disconnect the battery Now let’s increase the charge as a function of time 0 enc B dl i Maxwell’s genralization of Ampere’s Law
Lecture 21-5 Maxwell-Ampere Law We can combine Maxwell’s Law of Induction with Ampere’s Law to write which is called the Maxwell-Ampere Law (not surprisingly!) 0 enc B dl i  0 0 0 E enc d B dl i dt   00 E d B dl dt  – For the case of constant current, such as current flowing in a conductor, this equation reduces to Ampere’s Law – For the case of a changing electric field without current flowing, such as the electric field between the plates of a capacitor, this equation reduces to the Maxwell Law of Induction is the displacement current . 0 E d d i dt where Displacement Current 0 0 0 0 () E enc d enc d B d l i i i     

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Lecture 21-6 Maxwell’s Equations Basis for electromagnetic waves! 0 inside S Q E d A  0 S B d A B C d E dl dt    0 00 C E B l i d d Integral Form Differential Form 0 0 0 0 (1) (2) 0 (3) (4) ˆˆ ˆ E B EB t B E j t x y z x y z         is the charge density and j is the curent density
Lecture 21-7 Derivation of the Wave Equation 2 2 2 2 2 2 2 2 (3) : ( ) ( ) ( ) ( ) (1) 0 0 EB t BAC CAB rule A B C B A C C A B E E E E E x y z  

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Lecture21_Kim - Lecture 21-1 PHYS241 Question 1 November 8...

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