p34_075 - 75. We take the derivative with respect to x of...

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75. We take the derivative with respect to x of both sides of Eq. 34-11: ∂x µ ∂E ∂x = 2 E ∂x 2 = ∂x µ ∂B ∂t = 2 B ∂x∂t . Now we diFerentiate both sides of Eq. 34-18 with respect to t : ∂t µ ∂B ∂x = 2 B ∂x∂t = ∂t µ ε 0 µ 0 ∂E ∂t = ε 0 µ 0 2 E ∂t 2 . Substituting 2 E/∂x 2 = 2 B/∂x∂t from the ±rst equation above into the second one, we get ε 0 µ 0 2 E ∂t 2 = 2 E ∂x 2 , or 2 E ∂t 2 = 1 ε 0 µ 0 2 E ∂x 2 = c 2 2 E ∂x 2 . Similarly, we diFerentiate both sides of Eq. 34-11 with respect to
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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