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Unformatted text preview: 2 c I ( t ) Z s Z 1 2 s 1 rd 2 dr dz + 2 c I ( t ) Z s Z 1 2 s 1 rd 2 dr dz = 4 c I ( t ) Z s dz Z 1 2 s 1 rd 2 dr Φ( t ) = 4 s c I ( t ) ± ln ± 1 2 ( sd ) ²ln ±d s ²² Φ( t ) = 4 s c I et τ ln ± ds d ² Using the magnetic ﬂux through the loop we can ﬁnd the EMF on the loop. V ( t ) =d Φ dt = 4 s c I ± 1 τ ² et τ ln ± ds d ² 1 Now to ﬁnd the total charge that will ﬂow through any point in the loop we simply integrate the current in the loop over all time. Q = Z ∞ I loop dt = 1 R Z ∞ V ( t ) dt =1 R 4 s c I ln ± ds d ²Z ∞1 τ et τ dt Q = 4 s Rc I ln ± ds d ² (b.) To ﬁnd the work done on the loop we do the following. W tot = Z ∞ I 2 ( t ) R dt = Z ∞ 1 R V 2 ( t ) dt 2...
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This note was uploaded on 03/27/2008 for the course PY 415 taught by Professor Reynolds during the Spring '06 term at N.C. State.
 Spring '06
 reynolds

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