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**Electromagnetism Giancoli Ch.21-29 Physics of Astronomy, winter week 7**

Review of waves and wave equations Summary of EM & Maxwell’s eqns Derive EM wave equation and speed of light! Magnetic monopole more symmetry Today: to American Physical Society meeting! Next Friday 1:00-2:00 in 1050 Lab I: Science Carnival poster session

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Waves

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**Wave equation 1. Differentiate dD/dt d2D/dt2**

2. Differentiate dD/dx d2D/dx2 3. Find the speed from

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**Causes and effects of E Gauss: E fields diverge from charges**

Lorentz force: E fields can move charges F = q E

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**Causes and effects of B Ampere: B fields curl around currents**

Lorentz force: B fields can bend moving charges F = q v x B = IL x B

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**Changing fields create new fields!**

Faraday: Changing magnetic flux induces circulating electric field Guess what a changing E field induces?

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**Changing E field creates B field!**

Current piles charge onto capacitor Magnetic field doesn’t stop Changing electric flux “displacement current” magnetic circulation

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**Partial Maxwell’s equations**

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**Maxwell eqns electromagnetic waves**

Consider waves traveling in the x direction with frequency f= w/2p and wavelength l= 2p/k E(x,t)=E0 sin (kx-wt) and B(x,t)=B0 sin (kx-wt) Do these solve Faraday and Ampere’s laws?

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Faraday + Ampere

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**Sub in: E=E0 sin (kx-wt) and B=B0 sin (kx-wt)**

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**Speed of Maxwellian waves?**

Faraday: -wB0 = k E Ampere: m0e0wE0=kB0 Eliminate B0/E0 and solve for v=w/k e0 = 8.85 x C2 N/m2 m0 = 4 p x 10-7 Tm/A

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**Maxwell equations Light**

E(x,t)=E0 sin (kx-wt) and B(x,t)=B0 sin (kx-wt) solve Faraday’s and Ampere’s laws. Electromagnetic waves in vacuum have speed c and energy/volume = 1/2 e0 E2 = B2 /(2m0 )

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**Full Maxwell equations**

Notice the asymmetries – how can we make these symmetric by adding a magnetic monopole?

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