a1009 - ²(1 point(31 EM waves in vacuum 1 Use ² ijk...

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ADVANCED DYNAMICS — PHY 4241/5227 HOME AND CLASS WORK – SET 9 (30) SI units (due February 24 in class). 1. How is one second [s] defned (1 point)? 2. How is one meter [m] defned (1 point)? 3. How is one kilogram [kg] defned (1 point)? 4. How is one Newton [N] defned (1 point)? 5. How is one Ampere [A] defned (1 point)? 6. How is one Coulomb [C] defned (1 point)? 7. From the Biot-Savart law it ±ollows that the ±orce exerted by one (infnitely long) wrire on a section o± length l o± a parallel wire is given by F = μ 0 2 π I 1 I 2 d l , where μ 0 is the permeability of vacuum . What is the (exact) value o± μ 0 (1 point)? 8. Using the above units, Coulomb’s law read F ( r ) = κ 0 Q 1 Q 2 r 2 , κ 0 = 1 4 π ² 0 where κ 0 is called Coulomb constant and ² 0 permittivity of vacuum . They can, ±or instance, be estimated by ±orce measurements. In SI units ² 0 = 8 . 85418782 × 10 - 12 . What are the physical dimensions o±
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Unformatted text preview: ² (1 point)? (31) EM waves in vacuum 1. Use ² ijk notation and Einstein’s summation convention to show (due March 3 be±ore class). ∇ × ( ∇ × ~ A ) = ∇ ( ∇ · ~ A )- ∇ 2 ~ A (3 points) . 2. Use SI units and write down Maxwell’s equations in vacuum (2 points, March 3 in class). 3. Calculate ∇ × ( ∇ × ~ E ) to derive ∇ 2 ~ E = 1 v ∂ ∂t ! 2 ~ E with v = 1 √ μ ² (3 points , March 3 in class) . 4. Calculate v = 1 / √ ² μ and make an observation (2 points, March 3 in class). (32) Homework, due March 5 be±ore class (4 points). Repeat the previous consider-ations ±or ∇ × ( ∇ × ~ B ). Read the relativity notes up to Eq. (1.42), p.10 (due Monday March 15)....
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