1000 Solved Problems in Modern Physics

(Grace) #1

84 1 Mathematical Physics


N=6;


yn= 29 .5;


xn=3;


x^2 n= 19

xn^3 =27;


xn^4 =115;


xnyn= 21 .3;


x^2 nyn= 158. 1

Solving (1), (2) and (3) we finda 0 = 0 .582;a 1 =− 1 .182;a 2 = 1. 556

Fig. 1.18Least square fit of the parabola


1.102C=^2 πε^0
ln


(b
a

) (1)

From propagation of errors

σc=

[(

∂c
∂b

) 2

σb^2 +

(

∂c
∂a

) 2

σa^2

] 1 / 2

(2)

∂c
∂b

=−

c
blnba

;

∂c
∂a

=

c
alnba

(3)

Using (1), (2) and (3) and simplifying

σc
c

=

[(

ln

b
a

)]− 1 / 2 [

σa^2
a^2

+

σa^2
b^2

] 1 / 2

Substitutinga=10 mm,b=20 mm,σa=1 mm andσb=1mm,σc/c=
0. 16
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