# ps08 - Physics 2214 Problem Set#8(Due 11:15 am Thursday 1...

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Page 1 of 3 Physics 2214 Problem Set #8 (Due 11:15 am, Thursday 10/30/07) 1. YF derives the (1D) wave equation (on pp. 1099-1101) by assuming a plane wave propagating in the x direction that is polarized in the y direction. The second part of the derivation is based on applying Ampere’s law counterclockwise around rectangular loop efghe in the xz plane (Fig. 32.11, Eq. 32.13). We’re going to generalize this approach to do a major step in the derivation of the differential form of Ampere’s law from the integral form. (a) Generalize Eq. 32.13 by calculating d Bl G G v around the same loop but without any assumptions about the direction of B G or the direction of propagation. (In other words, let B G have x -, y -, and z -components and let it depend on x , y , z , and t .) Substitute Δ z for their a . (b) Divide d GG v by the area Δ x Δ z and take the limits Δ x 0 and Δ z 0 to show that the circulation per unit area is the y -component of the curl of B G ; i.e. show that () ,0 lim y xz d ΔΔ→ =∇× ΔΔ B G G G v [We won’t do the rest of the derivation, but it goes like this: Applying Ampere’s law to this loop yields () () 00 / y y Et εμ ∇× = B G . We can then take loops in the

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ps08 - Physics 2214 Problem Set#8(Due 11:15 am Thursday 1...

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