Question

Only need solve the underline parts.please give full explanations.Why and how many terms might required.  Other parts are DONE.

1. Equation 12 shows two expressions for a magnetic field produced by a current carrying wire. One of them is approximated by assum- ing L > x (Bapprox (x)) while the other is exact (Bexact (x)). Produce a plot of these two expressions as a function of x from x = L/10 to 2L assuming L = I = 1. What is the percentage difference of the magnetic field between the two expressions when x = L? Do you think the approximation still yields a good prediction? What about when x = L/10? 2. Using the full expression for the magnetic field given in equation 12, carry out the binomial expansion to the next highest term in the expansion. Does this agree with the percent error found above when x = L? How many terms might be required to give you the error when x = L? When x = L/10? LI B = Ho = = Mo 21 5V1+ 4x2 / 12 – 47 x (1 +4x2/L2)-1/2 Mo 21 47 x

Answer 1

Given that

Assume L>>x(B_approx(x))

L>>(B_exact(x))

x=L/10 to 2L

L=I=1

  
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2.0(0.9805806) Besact(*) = x 19.611 --a) Bappsor (*) = Bapprox (N) = x 20 - (b) i At x=qL, x=2 (²2=1) (1+4x2?)\2 Bexact (N) = not The (1+16) V2 = tem o (11312 Bexact(x)= 40 x0.24953 --(5) Bappxox (x) = auto (d) Bapprox (x) , Bexact (x) Mox200 X 19.611 HTT X = 2 MO HT Hox0.24253

So, at x=1 Ho 2% (+4) - - 4T L5 Mo 2I , Bexact(x) = ? Bappogox = | behact - bеff%ss } 1 dislebence - X (Bexact + Bappxox)/2 100 % = ( ) X100 = ( ) x100 19 Titus 2 11-9-23606 1+2-93606 X 100 Yo difference = 76.391.

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Bappbox (x) - Mo 201 HT Bionomial expansion expression, B(x) = more I ( 1+ ux%, 2)\/2 at x= 2/10, Bla) = no 2.176 (174(+)?/12) VE Mo gol lit4b 719,1-1/2 MTT I 100 / = pot interesele ma e 201 (1+0-04)/2 - na po 209 (1 - 0.04 + (0-04) ---) B1%) = 40 201 (1+6.0194) so I we require order only terms upto second for x= 1 16