11hw - Solutions to problem set 11(141A Sp07 1 1(ISSP 8.4...

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Solutions to problem set 11 (141A Sp07) 1 1. (ISSP 8.4). Note that from the symmetry of the problem it doesn’t matter where in the xy plane the B-field points. Therefore we will choose it to lie along the x-axis. Using ISSP page 198 equation 29: ˙ v i = m - 1 ij F j we get ˙ v y = m - 1 yy ( - e )( ~ v × ~ B ) y = (1 / m t )( - e ) v z B ˙ v z = m - 1 zz ( - e )( ~ v × ~ B ) z = (1 / m l )( e ) v y B Therefore ¨ v y = ( - e / m t ) ˙ v z B = - e 2 B 2 m t m l v y Since the particle is executing simple harmonic motion, ¨ v y = - ω 2 v y . Then ω 2 = e 2 B 2 m t m l ω = eB m t m l 2. (ISSP 8.5). (a) We must add together the contributions of the electrons and holes. Then j x j y j z = σ e 0 ( ω e c τ e ) 2 1 - ω e c τ e 0 ω e c τ e 1 0 0 0 ( ω e c τ e ) 2 + σ h 0 ( ω h c τ h ) 2 1 ω h c τ h 0 - ω h c τ h 1 0 0 0 ( ω h c τ h ) 2
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