ps2soln - ELEC 262 2009 Problem set 2 solutions 1(a) The...

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ELEC 262 2009 Problem set 2 solutions 1(a) The complex amplitude is everything other than exp{j(kz- ω t)}. It is given by () ( ) 0.4 0 ˆˆ 200 / =+ ± j Ex y V m e . (b) The B field is the same as the E field except that the direction is perpendicular, and the magnitude is smaller by a factor of the speed. So: ( ) ( ) ( ) ( ) 7- 1 1 5 8 77 - 1 1 5 200 / , , , cos 1.307 10 m 2.772 10 sec 0.4 2.121 10 / 9.43 10 0.4 =−+ × × + × × × × + / Vm Bxyzt x y z t ms xy T e s l a z t This field is less than 1 microTesla, so it is more than 50 times smaller than the earth’s static field. (c) The divergence is given by: ∂∂ ++ ∂∂∂ y x z E E E x yz . This field has E z = 0, and furthermore E x and E y depend only on z, not on x or y. Thus all three derivatives in this sum vanish. Obviously, the field has to satisfy 0 ∇⋅ = ±± E because that’s one of Maxwell’s equations. 2(a) To find the peak wavelength, we start with the blackbody formula (lecture 5, slide 14), differentiate, and set this equal to zero: 33 2 3 2 3 88 3 0 11 1 ν νν ν   πν π ν ν  == =    hk T T T T dI d h c h e h kT dd e c e e which looks much simpler if we define x T , and cancel out the constants in front: 23 2 3 0 1 1 −= x x x xx e e e This is equivalent to: 1 3 x x e
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This note was uploaded on 11/23/2009 for the course ELEC 262 taught by Professor Mittleman during the Spring '09 term at Rice.

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ps2soln - ELEC 262 2009 Problem set 2 solutions 1(a) The...

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