Equation (2-1), 



L 

 C = - 



T 



Therefore, equating (2-1) and (2-3), 



h = II tanh ^ 

 T 2tt \ L / 



2 

 and multiplying both sides by (lit) /LT 



(2ii)2 L (2it)2 gT /2Trd^ 



= — tanh 



LT T LT 2Tr y L ^ 



Hence , 



M" . ^ tanh l^\ 



(b) Equation (2-13) may be written 



gTH cosh[2Tr(z + d)/L] / 2ttx 2irt^ 



u = : : cos 



2L cosh(2ird/L) V L T , 



1 gH cosh[2Ti(z + d)/L] / 2Trx 2iTt^ 



u = : cos 



C 2 cosh(2Trd/L) \ L T - 



since 



Since 



T _ 1 

 L ~ C 



C = II tanh -^ 

 2. [l I 



irH 1 cosh[2TT(z + d)/L] /2iix 2TTt'^ 



U = ; ; COS I 



T tanh(27rd/L) cosh(2Trd/L) \ L T , 



and since 



'2Trd\ sinh(2TTd/L) 



tanh 



L, / cosh(2Trd/L) 

 therefore, 



ttH cosh[2iv(z + d)/L] /2Trx 2Trt^ 



u = : ; cos 



T sinh(2Trd/L) V L T 



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2-19 



