part 1 of 2 Consider the field due to a uniformly charged disk of radius R. and charge Q. Along the symmetry axis at distance z from the cen- ter, the field has been written in following forms. where Eexact = Eo E1 Eo part 2 of 2 2 R² +2² (1-1/2) (Q/A) 200 Eo To compare the accuracy of different ap- proximations it is convenient to work with the normalized difference to be specified below. The nth order smallness is charac- terized by e" and € = with being the R 2 smallness parameter. In general the nth or- der term takes the form Ce", where C is some finite constant (e.g 0.1

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part 1 of 2
Consider the field due to a uniformly
charged disk of radius R. and charge Q. Along
the symmetry axis at distance z from the cen-
ter, the field has been written in following
forms.
where
Eexact
=
Eo
E₁ Eo
part 2 of 2
2
R² + z²
(1-7)
(Q/A)
280
Eo =
To compare the accuracy of different ap-
proximations it is convenient to work with
the normalized difference to be specified
below. The nth order smallness is charac-
terized by e" and € = with being the
R
smallness parameter. In general the nth or-
der term takes the form Ce", where C is some
finite constant (e.g 0.1 < C < 10).
Eexact - E1|
For the normalized difference
Eo
identify the correct choice among the follow-
ing
|E1 - Eo
For the normalized difference
Eo
identify the correct choice among the follow-
ing
1.
2. €³
3. €2
4. €
1. €
2. €³
3. €²
4. €4
Transcribed Image Text:part 1 of 2 Consider the field due to a uniformly charged disk of radius R. and charge Q. Along the symmetry axis at distance z from the cen- ter, the field has been written in following forms. where Eexact = Eo E₁ Eo part 2 of 2 2 R² + z² (1-7) (Q/A) 280 Eo = To compare the accuracy of different ap- proximations it is convenient to work with the normalized difference to be specified below. The nth order smallness is charac- terized by e" and € = with being the R smallness parameter. In general the nth or- der term takes the form Ce", where C is some finite constant (e.g 0.1 < C < 10). Eexact - E1| For the normalized difference Eo identify the correct choice among the follow- ing |E1 - Eo For the normalized difference Eo identify the correct choice among the follow- ing 1. 2. €³ 3. €2 4. € 1. € 2. €³ 3. €² 4. €4
Expert Solution
Step 1: To know the given

All the fields are given in part 1 introduction.

Now, the normalized difference  fraction numerator vertical line square root of blank end root E subscript e x a c t end subscript minus E subscript 1 vertical line over denominator E subscript o end fraction equals fraction numerator vertical line E subscript o left parenthesis 1 minus fraction numerator z over denominator square root of R squared plus z squared end root end fraction right parenthesis minus E subscript o left parenthesis 1 minus z over R right parenthesis vertical line over denominator E subscript o end fraction
space space space space space space space space space space space space space space space space space space space space space space equals space z over R minus fraction numerator z over denominator R square root of 1 plus z squared over R squared end root end fraction
L e t space z over R equals epsilon
N o w comma space fraction numerator vertical line E subscript e x a c t end subscript minus E subscript 1 vertical line over denominator E subscript o end fraction equals epsilon minus fraction numerator epsilon over denominator square root of 1 plus epsilon squared end root end fraction

here epsilon is the smallness parameter. Then the second is also very small and negligible.

Therefore, the normalized difference is ϵ

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