7 em waves in vacuum the differential form of gausss

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Unformatted text preview: Sun to the Earth? 7. EM Waves in Vacuum. The differential form of Gauss’s law is ρ ￿￿ ∇·E = ￿0 ￿￿ ￿ where ∇ · E is called the divergence of E and can be expressed in rectangular coordinates as ￿￿ ∇·E = ￿ ∂∂∂ , , ∂x ∂y ∂z ￿ · (Ex , Ey , Ez ) = ∂ Ex ∂ Ey ∂ Ez + + ∂x ∂y ∂z Suppose that a plane EM wave travels in the +x direction in vacuum (ρ= 0). Then electric field components are functions of (x – ct): ￿ E = f (x − ct)ˆ + g (x − ct)ˆ + h(x − ct)ˆ x y z Physics 2214, Spring 2012 3 Cornell University TA's Name:_____________________________________Section: ____ Your Name: ____________________________________ What does Gauss’s law let you conclude about the functions f, g, and/or h? (You ￿ can use Gauss's law for magnetic fields to make a similar conclusion about B .) 8. Faraday’s law and EM waves. Consider Faraday’s law ￿ ∂B ￿ ￿ ∇×E =− ∂t Suppose that the magnetic field points in the y direction (such that Bx and Bz are zero), and that the electric field is of the form ￿ E = f (x − ct)ˆ + g (x − ct)ˆ + h(x − ct)ˆ x y z ￿ as in problem 4. What does Faraday’s law allow you to conclude about E ? Questions, Exercises and Problems from Y&F 12th Ed. for study and review: (Do not turn these in!) Volume 1, Chapter 15: Questions 13, 16, 18 Exercises 21, 24 Problems 63, 64, 65, 66, 81, 84 Volume 1, Chapter 16: Questions: 17, 18, 20 Exercises 17, 19, 21, 22, 43, 44, 46, 49, 50 Problems 74, 75, 77, 79, 80 Volume 2, Chapter 32: Questions 32.1, 32.6 32.9, 32.10. Exercises 2, 6, 8, 9, 35 Problems 36, 55 Physics 2214, Spring 2012 4 Cornell University...
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This note was uploaded on 02/27/2013 for the course PHY 2214 taught by Professor Davis during the Spring '12 term at Cornell University (Engineering School).

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