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Êà-÷å-ñòâåí-íîå ðàñ-õîæ-äå-íèå íà ñðåä-íèõ ÷à-ñòî-òàõ ìî- +æåò áûòü ñâÿ-çà-íî ñ "ïå-ðå-õî-äîì"ðåøåíèÿ + [] + +[8] [9] +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 761. +Package atveryend Info: Empty hook `AfterLastShipout' on input line 761. + (./lab371.aux) +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 761. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 761. +Package rerunfilecheck Info: File `lab371.out' has not changed. +(rerunfilecheck) Checksum: 37CB11BC8FB1F40F9D37C74029F98DD3;2926. + + +LaTeX Font Warning: Some font shapes were not available, defaults substituted. + + +LaTeX Warning: There were multiply-defined labels. + +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 761. + ) +Here is how much of TeX's memory you used: + 34447 strings out of 482657 + 765820 string characters out of 5957839 + 1303672 words of memory out of 5000000 + 48763 multiletter control sequences out of 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+\usepackage[a4paper,top=1.3cm,bottom=2cm,left=1.5cm,right=1.5cm,marginparwidth=0.75cm]{geometry} +%%% Работа Ñ Ñ€ÑƒÑÑким Ñзыком +\usepackage{cmap} % поиÑк в PDF +\usepackage[warn]{mathtext} % руÑÑкие буквы в фомулах +\usepackage[T2A]{fontenc} % кодировка +\usepackage[utf8]{inputenc} % кодировка иÑходного текÑта +\usepackage[english,russian]{babel} % Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð°Ñ†Ð¸Ñ Ð¸ переноÑÑ‹ +\usepackage{physics} +\usepackage{multirow} + +%%% Ðормальное размещение таблиц (пиÑать [H] в окружении таблицы) +\usepackage{float} +\restylefloat{table} + + +\usepackage{graphicx} + +\usepackage{wrapfig} +\usepackage{tabularx} + +\usepackage{hyperref} +\usepackage[rgb]{xcolor} +\hypersetup{ + colorlinks=true,urlcolor=blue +} + +%%% Ð”Ð¾Ð¿Ð¾Ð»Ð½Ð¸Ñ‚ÐµÐ»ÑŒÐ½Ð°Ñ Ñ€Ð°Ð±Ð¾Ñ‚Ð° Ñ Ð¼Ð°Ñ‚ÐµÐ¼Ð°Ñ‚Ð¸ÐºÐ¾Ð¹ +\usepackage{amsmath,amsfonts,amssymb,amsthm,mathtools} % AMS +\usepackage{icomma} % "УмнаÑ" запÑтаÑ: $0,2$ --- чиÑло, $0, 2$ --- перечиÑление + +%% Ðомера формул +%\mathtoolsset{showonlyrefs=true} % Показывать номера только у тех формул, на которые еÑть \eqref{} в текÑте. + +%% Шрифты +\usepackage{euscript} % Шрифт Евклид +\usepackage{mathrsfs} % КраÑивый матшрифт +\usepackage{pgfplots} +\pgfplotsset{compat=1.9} + +%% Свои команды +\DeclareMathOperator{\sgn}{\mathop{sgn}} + +%% ÐŸÐµÑ€ÐµÐ½Ð¾Ñ Ð·Ð½Ð°ÐºÐ¾Ð² в формулах (по ЛьвовÑкому) +\newcommand*{\hm}[1]{#1\nobreak\discretionary{} + {\hbox{$\mathsurround=0pt #1$}}{}} + +\date{\today} + +\begin{document} + +\begin{titlepage} + \begin{center} + {\large МОСКОВСКИЙ ФИЗИКО-ТЕХÐИЧЕСКИЙ ИÐСТИТУТ (ÐÐЦИОÐÐЛЬÐЫЙ ИССЛЕДОВÐТЕЛЬСКИЙ УÐИВЕРСИТЕТ)} + \end{center} + \begin{center} + {\large Физтех-школа физики и иÑÑледований им. Ландау} + \end{center} + + + \vspace{4.5cm} + {\huge + \begin{center} + {\bf Отчёт о выполнении лабораторной работы â„–3.7.1}\\ + Скин-Ñффект в полом цилиндре + \end{center} + } + \vspace{2cm} + \begin{flushright} + {\LARGE Ðвтор:\\ СтавиÑÑкий Георгий Леонидович \\ + \vspace{0.2cm} + Б02-103} + \end{flushright} + \vspace{8cm} + \begin{center} + Долгопрудный\\ + \today + \end{center} +\end{titlepage} + +\section{Введение} + +\textbf{Цель работы:} иÑÑледование Ð¿Ñ€Ð¾Ð½Ð¸ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ñ Ð¿ÐµÑ€ÐµÐ¼ÐµÐ½Ð½Ð¾Ð³Ð¾ магнитного Ð¿Ð¾Ð»Ñ Ð² полый медный цилиндр. +\\ +\textbf{Ð’ работе иÑпользуютÑÑ:} генератор звуковой чаÑтоты, Ñоленоид, намотанный на полый цилиндричеÑкий ÐºÐ°Ñ€ÐºÐ°Ñ Ð¸Ð· диÑлектрика, медный Ñкран в виде трубки, Ð¸Ð·Ð¼ÐµÑ€Ð¸Ñ‚ÐµÐ»ÑŒÐ½Ð°Ñ ÐºÐ°Ñ‚ÑƒÑˆÐºÐ°, амперметр, вольтметр, оÑциллограф. + +\section{ТеоретичеÑкие ÑведениÑ} + +\begin{wrapfigure}{r}{4cm} + \includegraphics[width=4cm]{Screenshot_1.png} + \label{pic:2} +\end{wrapfigure} + +Ð’ работе изучаетÑÑ Ñвление Ñкин-Ñффекта в длинном медном тонкоÑтенном цилиндре, помещенном в Ñоленоид. Будем Ñчитать цилиндр доÑтаточно длинным и пренебрегать краевыми Ñффектами, в Ñтом приближении $H$ вÑюду направлено по оÑи Ñимметрии ÑиÑтемы, а $E$ - перпендикулÑрно радиуÑу. Будем Ñчитать, что Ñти Ð¿Ð¾Ð»Ñ ÐºÐ¾Ð»ÐµÐ±Ð»ÑŽÑ‚ÑÑ Ð¿Ð¾ гармоничеÑкому закону Ñ Ñ‡Ð°Ñтотой задаваемой током в Ñоленоиде: + +\begin{equation} + H_z = H(r)e^{iwt} +\end{equation} + +\begin{equation} + E = E(r)e^{iwt} +\end{equation} + +ПуÑть Ñ€Ð°Ð´Ð¸ÑƒÑ Ñ†Ð¸Ð»Ð¸Ð½Ð´Ñ€Ð° $a$, толщина Ñтенки $h << a$, тогда можно ограничитьÑÑ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑ€Ð½Ñ‹Ð¼ решением задачи о Ñкин-Ñффекте. Внутри цилиндра токи отÑутÑтвуют, поÑтому поле однородно и $H(r) = H_1 = const$. ВоÑпользуемÑÑ Ð¸Ð½Ñ‚ÐµÐ³Ñ€Ð°Ð»ÑŒÐ½Ñ‹Ð¼ законом Ñлектромагнитной индукции и получим ÑвÑзь ÑлектричеÑкого и магнитных полей на внутренней границе цилиндра: + +\begin{wrapfigure}{r}{4cm} + \includegraphics[width=4cm]{Screenshot_2.png} + \label{pic:2} +\end{wrapfigure} + +\begin{equation} + E\cdot 2\pi r = -\mu_0\pi r^2 \cdot \frac{dH_z}{dt} +\end{equation} + +\begin{equation} + E_1 = -\frac{1}{2}iwa\mu_0 H_1 +\end{equation} + +Поле внутри Ñтенки цилиндра будет опиÑыватьÑÑ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑ€Ð½Ñ‹Ð¼ уравнением диффузии полÑ: + +\begin{equation} + \frac{d^2H}{dx^2} = iw\sigma\mu_0H +\end{equation} + +Данное уравнение вмеÑте Ñ ÐºÑ€Ð°ÐµÐ²Ñ‹Ð¼Ð¸ уÑловиÑми $H_0$ и $H_1$ полноÑтью определÑет Ð¿Ð¾Ð»Ñ Ð² Ñтенке. Стоит отметить, что $H_0$ завиÑит только от тока в обмотке Ñоленоида. Тогда: + +\begin{equation} + H(x) = Ae^{\alpha x} + Be^{-\alpha x} +\end{equation} + +\begin{equation} + \alpha = \sqrt{iw\sigma\mu_0} = \frac{1 + i}{\delta} = \frac{\sqrt{2}e^{i\frac{\pi}{4}}}{\delta} +\end{equation} + +$\delta$ здеÑÑŒ - толщина Ñкин ÑлоÑ, на которой амплитуды полей Ñпадают в $e$ раз. Первое граничное уÑловие дает $A + B = H_0$, иÑÐ¿Ð¾Ð»ÑŒÐ·ÑƒÑ Ñто можно преобразовать выражение(6): + +\begin{equation} + H(x) = H_0e^{-\alpha x} + 2Bsh(\alpha x) +\end{equation} + +Далее, воÑпользовавшиÑÑŒ законом Ðмпера в одномерном варианте $E(x) = \frac{1}{\sigma}\frac{\partial H}{\partial x}$, мы можем иÑÐ¿Ð¾Ð»ÑŒÐ·ÑƒÑ ÑÐ¾Ð¾Ñ‚Ð½Ð¾ÑˆÐµÐ½Ð¸Ñ Ð½Ð° $E_1$ и $H_1$, полученное ранее, иÑключить конÑтанту и в итоге получить: + +\begin{equation} + H_1 = \frac{H_0}{ch(\alpha h) + \frac{1}{2}\alpha a sh(\alpha h) } +\end{equation} + +Далее Ñледует раÑÑмотреть предельные Ñлучаи: + +1. ЧаÑтота тока в Ñоленоиде мала, $\delta >> h$, тогда: + +\begin{equation} + \frac{|H_1|}{|H_0|} = \frac{1}{\sqrt{1 + \frac{1}{4}(ah\sigma \mu_0 w)^2}} +\end{equation} + +\begin{equation} + tg(\psi) = \frac{ah}{\sigma^2} +\end{equation} + +$\psi$ - разноÑть фаз $H_1$ и $H_0$. + +2. ЧаÑтота тока в Ñоленоиде выÑока, $\delta << h$, тогда: + +\begin{equation} + \frac{H_1}{H_0} = \frac{2\sqrt{2}\delta}{a}e^{-\frac{h}{\delta}}e^{-i(\frac{\pi}{4} + \frac{h}{\delta})} +\end{equation} + +\begin{equation} + \psi = \frac{\pi}{4} + h\sqrt{\frac{w\sigma \mu_0}{2}} +\end{equation} + +Скин Ñффект также оказывает влиÑние на индуктивноÑть катушки: + +\begin{equation} + \Phi = \Phi_{out} + \Phi_{in} = H_0S_0 + H_1S_1 = LI +\end{equation} + +Ð£Ñ‡Ð¸Ñ‚Ñ‹Ð²Ð°Ñ Ð½ÐµÐ·Ð°Ð²Ð¸ÑимоÑть внешнего потока от чаÑтоты, можем запиÑать: + +\begin{equation} + \L_{min} = \frac{\Phi_{out}}{I} +\end{equation} + +Ðайдем Ñоотноошение потоков: + +\begin{equation} + \Phi_{in} = H_1S_1 = \Phi_{out}\frac{S_1}{nS_0} +\end{equation} + +Где n - отношение напрÑженноÑти Ð¿Ð¾Ð»Ñ Ñнаружи и внутри цилиндра. МакÑимальное поле доÑтигаетÑÑ Ð¿Ñ€Ð¸ $H_0 = H_1$, поÑтому: + +\begin{equation} + \Phi_{max} = H_0(S_0 + S_1) = L_{max}I +\end{equation} + +и тогда: + +\begin{equation} + \frac{S_1}{S_0} = \frac{L_{max} - L_{min}}{L_{min}} +\end{equation} + +ИÑÐ¿Ð¾Ð»ÑŒÐ·ÑƒÑ (14) и (18), а также ÑÐ¾Ð¾Ñ‚Ð½Ð¾ÑˆÐµÐ½Ð¸Ñ Ñ€Ð°Ð½ÐµÐµ: + +\begin{equation} + \frac{L_{max} - L}{L - L_{min}} = \pi^2a^2h^2\mu_0^2\sigma^2\nu^2 +\end{equation} + + + + +\section{ЭкÑÐ¿ÐµÑ€Ð¸Ð¼ÐµÐ½Ñ‚Ð°Ð»ÑŒÐ½Ð°Ñ ÑƒÑтановка} + +\begin{wrapfigure}{r}{6.5cm} + \includegraphics[width=6.5cm]{Screenshot_3.png} +\end{wrapfigure} + + +Схема ÑкÑпериментальной уÑтановки Ð´Ð»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ñ€Ð¾Ð½Ð¸ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ñ Ð¿ÐµÑ€ÐµÐ¼ÐµÐ½Ð½Ð¾Ð³Ð¾ магнитного Ð¿Ð¾Ð»Ñ Ð² медный полый цилиндр изображена на риÑ. 4. Переменное магнитное поле ÑоздаётÑÑ Ñ Ð¿Ð¾Ð¼Ð¾Ñ‰ÑŒÑŽ Ñоленоида, намотанного на полый цилиндричеÑкий ÐºÐ°Ñ€ÐºÐ°Ñ 1 из поливинилхлорида, который подключаетÑÑ Ðº генератору звуковой чаÑтоты. Внутри Ñоленоида раÑположен медный цилиндричеÑкий Ñкран 2. Ð”Ð»Ñ Ð¸Ð·Ð¼ÐµÑ€ÐµÐ½Ð¸Ñ Ð¼Ð°Ð³- +нитного Ð¿Ð¾Ð»Ñ Ð²Ð½ÑƒÑ‚Ñ€Ð¸ Ñкрана иÑпользуетÑÑ Ð¸Ð·Ð¼ÐµÑ€Ð¸Ñ‚ÐµÐ»ÑŒÐ½Ð°Ñ ÐºÐ°Ñ‚ÑƒÑˆÐºÐ° 3. Ðеобходимые параметры Ñоленоида, Ñкрана и измерительной катушки указаны на уÑтановке. ДейÑтвующее значение переменного тока в цепи +Ñоленоида измерÑетÑÑ Ð°Ð¼Ð¿ÐµÑ€Ð¼ÐµÑ‚Ñ€Ð¾Ð¼ Ð, а дейÑтвующее значение напрÑÐ¶ÐµÐ½Ð¸Ñ Ð½Ð° измерительной катушке измерÑет вольтметр V. Ð”Ð»Ñ Ð¸Ð·Ð¼ÐµÑ€ÐµÐ½Ð¸Ñ Ñдвига фаз между током в цепи Ñоленоида и напрÑжением на измерительной катушке иÑпользуетÑÑ Ð´Ð²ÑƒÑ…ÐºÐ°Ð½Ð°Ð»ÑŒÐ½Ñ‹Ð¹ оÑциллограф. Ðа вход одного канала подаётÑÑ Ð½Ð°Ð¿Ñ€Ñжение Ñ Ñ€ÐµÐ·Ð¸Ñтора R, которое пропорционально току, а на вход второго канала - напрÑжение Ñ Ð¸Ð·Ð¼ÐµÑ€Ð¸Ñ‚ÐµÐ»ÑŒÐ½Ð¾Ð¹ катушки. + +Заметим некоторые ÑоотношениÑ, которые будет удобно измерÑть в ходе ÑкÑперимента: + +Ð”Ð»Ñ Ð½Ð°Ð¿Ñ€ÑÐ¶ÐµÐ½Ð¸Ñ Ð½Ð° измерительной катушке, Ñправедливо: + +\begin{equation} + U = -SN\frac{dB_1}{dt} = -iw\mu_0 SNH_1 e^{iwt} +\end{equation} + +Тогда измерерÑÐµÐ¼Ð°Ñ Ð²Ð¾Ð»ÑŒÑ‚Ð¼ÐµÑ‚Ñ€Ð¾Ð¼ величина(уÑреднение по времени переменного напрÑжениÑ): + +\begin{equation} + U = \frac{SNw}{\sqrt{2}}\mu_0|H_1| +\end{equation} + +То еÑть: + +\begin{equation} + |H_1|\propto \frac{U}{\nu} +\end{equation} + +При Ñтом: + +\begin{equation} + |H_0|\propto I +\end{equation} + +Тогда очевидно: + +\begin{equation} + \frac{|H_1|}{|H_0|} = const\cdot \frac{U}{\nu I} +\end{equation} + +КонÑтанту из ÑÐ¾Ð¾Ñ‚Ð½Ð¾ÑˆÐµÐ½Ð¸Ñ Ð²Ñ‹ÑˆÐµ далее будем обозначать $\xi_0$. + +РазноÑть фаз магнитных полей на границе и в полоÑти цилиндра в ходе ÑкÑперимента определÑетÑÑ Ñ Ð¿Ð¾Ð¼Ð¾Ñ‰ÑŒÑŽ оÑциллографа. ДелениÑ, за которые ток в обмотках, фикÑирующийÑÑ Ñ‡ÐµÑ€ÐµÐ· амперметр, проходит половину фазы, обозначаетÑÑ Ð´Ð°Ð»ÐµÐµ за $X$, а минимальное раÑÑтоÑние между нулÑми тока и напрÑÐ¶ÐµÐ½Ð¸Ñ Ð² измерительной катушке внутри Ñоленоида за $X_0$. Тогда очевидно: + +\begin{equation} + \psi = \frac{X_0}{X} \cdot \pi - \pi/2 +\end{equation} + +Вычитание $\pi / 2$ ÑвÑзанно Ñ Ñ‚ÐµÐ¼, что напрÑжение на катушке - Ñто Ð¿Ñ€Ð¾Ð¸Ð·Ð²Ð¾Ð´Ð½Ð°Ñ Ð¿Ð¾ времени Ð¿Ð¾Ð»Ñ Ð²Ð½ÑƒÑ‚Ñ€Ð¸, что дает дополнительную прибавку к фазе $\pi / 2$. + + +\section{Ход работы} + +\subsection{Определение $\xi_0$ и $\sigma$ по низким чаÑтотам} + +Сначала оценим чаÑтоту, на которой $\delta = h$, Ð¿Ð¾Ð»Ð°Ð³Ð°Ñ $\sigma = 5\cdot10^{7}$ См/м, иÑÐ¿Ð¾Ð»ÑŒÐ·ÑƒÑ Ñ„Ð¾Ñ€Ð¼ÑƒÐ»Ñƒ (7): + +\begin{equation} + \nu = \frac{1}{\pi h^2\sigma \mu_0} \approx 2250 \text{ Гц} +\end{equation} + +Так как вÑе вычиÑÐ»ÐµÐ½Ð¸Ñ Ð² обработке ÑводÑÑ‚ÑÑ Ðº иÑпользованию одних и тех же данных, предÑтавленных в различных чаÑтотных диапазонах, будет удобно ÑвеÑти вÑе Ð½Ð°Ð±Ð»ÑŽÐ´ÐµÐ½Ð¸Ñ Ð² Ñерию таблиц: + +Далее + +\begin{table}[H] + \centering + \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} + \hline + $ \nu $, Гц & 22.5 & 32.5 & 42.5 & 50 & 60 & 70 & 80 & 90 & 100 & 110 \\ \hline + $ U $, Ð’ & 0.1555 & 0.2207 & 0.2817 & 0.3246 & 0.3776 & 0.4255 & 0.4686 & 0.5069 & 0.5409 & 0.5708\\ \hline + $ I $, мР& 435.4 & 432.5 & 427.9 & 424.0 & 418.2 & 412.0 & 405.8 & 399.5 & 393.4 & 387.4 \\ \hline + $ X $ & - & - & - & - & - & - & - & - & - & - \\ \hline + $ X_0 $ & - & - & - & - & - & - & - & - & - & - \\ \hline + \end{tabular} + \caption{Результаты измерений до 0.5 $\nu_h$ - 1} + \label{tab:my-table1} +\end{table} + +\begin{table}[H] + \centering + \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} + \hline + $ \nu $, Гц & 130 & 153 & 176 & 200 & 225 & 300 & 400 & 500 & 600 & 700 & 800 \\ \hline + $ U $, Ð’ & 0.6202 & 0.6634 & 0.6957 & 0.7208 & 0.7402 & 0.7725 & 0.7870 & 0.7871 & 0.7801 & 0.7720 & 0.7581 \\ \hline + $ I $, мР& 376.0 & 364.9 & 355.8 & 347.8 & 341.0 & 326.4 & 314.3 & 305.7 & 298.3 & 292.5 & 285.5 \\ \hline + $ X $ & 1.4 & 2.4 & 2.2 & 2.1 & 1.8 & 3.9 & 2.8 & 1.9 & 4.4 & 3.7 & 3.2 \\ \hline + $ X_0 $ & 1.8 & 3.2 & 2.8 & 2.5 & 2.2 & 3.3 & 2.4 & 2 & 4.2 & 3.6 & 3.1 \\ \hline + \end{tabular} + \caption{Результаты измерений до 0.5 $\nu_h$ - 2} + \label{tab:my-table1} +\end{table} + +\begin{table}[H] + \centering + \begin{tabular}{|c|c|c|c||c|} + \hline + $ \nu $, Гц & 900 & 950 & 1000 & 1120 \\ \hline + $ U $, Ð’ & 0.7439 & 0.735 & 0.7271 & 0.706 \\ \hline + $ I $, мР& 278.5 & 275.0 & 271.5 & 263.0 \\ \hline + $ X $ & 2.8 & 2.6 & 2.5 & 4.4 \\ \hline + $ X_0 $ & 2.7 & 2.6 & 2.4 & 4.4 \\ \hline + \end{tabular} + \caption{Результаты измерений до 0.5 $\nu_h$ - 3} + \label{tab:my-table1} +\end{table} + +ПоÑтроим по данным первых двух таблиц график $\frac{1}{\xi^2}$ от $\nu^2$ и иÑпользуем точки от 22.5 до 400 Гц Ð´Ð»Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ аппрокÑимации (далее наблюдаютÑÑ Ñерьезные Ð¾Ñ‚ÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ñ Ð¾Ñ‚ линейноÑти завиÑимоÑти). ПогрешноÑть Ð´Ð»Ñ Ð·Ð½Ð°Ñ‡ÐµÐ½Ð¸Ð¹ была взÑта как их Ñупремум: + + + +\begin{center} + \begin{tikzpicture} + \begin{axis}[ + title={График 1 \quad График завиÑимоÑти $ \frac{1}{\xi^2}(\nu^2) $}, + xlabel={$ \nu^2 $, Гц $ ^2 $}, + ylabel={$\frac{1}{\xi^2}$}, + legend pos=south east, + xmajorgrids=true, + ymajorgrids=true, + grid style=dashed, + width = 520, + height = 350, + %xmin = 300, + %xmax = 335, + %ymin =40, + %ymax =135, + ] + \legend{ + ЭкÑпериментальные данные, + ÐппрокÑÐ¸Ð¼Ð°Ñ†Ð¸Ñ Ð´Ð°Ð½Ð½Ñ‹Ñ… + }; + \addplot [black, only marks, mark size = 2pt, + error bars/.cd, + x dir=both, x explicit, + y dir=both, y explicit, + ] table [x = T, y = sigma, y error plus = YError, y error minus = YError] { + T sigma YError + 506.25 3969 152 + 1056.25 4056.3 152 + 1806.25 4167.6 152 + 2500 4265 152 + 3600 4415.8 152 + 4900 4594 152 + 6400 4799.5 152 + 8100 5031.2 152 + 10000 5289.7 152 + 12100 5573.6 152 + 16900 6211.5 152 + 23409 7082.4 152 + 30976 8102.0 152 + 40000 9313.0 152 + 50625 10744.2 152 + 90000 16067.4 152 + 160000 25518.5 152 + }; + \addplot [blue, domain=0:160000, line width =3.2pt] {0.1349*x + 3926.4}; + \end{axis} + \end{tikzpicture} +\end{center} + +: +\[ k = (0.1349 \pm 0.001). \] +\[ b = (3926.4 \pm 152). \] + +По полученному значению Ñлементарно раÑÑчитаем $\xi_0$: + +\begin{equation} + \xi_0 = \sqrt{b} = 62.7 \pm 1.2 +\end{equation} + +и иÑÐ¿Ð¾Ð»ÑŒÐ·ÑƒÑ Ð¿Ð¾Ð»ÑƒÑ‡ÐµÐ½Ð½Ñ‹Ð¹ коÑффициент k и Ñоотношение (10), получаем Ð´Ð»Ñ $\sigma$: + +\begin{equation} + \sigma = \frac{\sqrt{k}}{\xi_0} \cdot \frac{1}{\pi ah\mu_0} \approx 4.71 \pm 0.3 \cdot 10^7 \text{ См/м} +\end{equation} + + +\subsection{Определение $\sigma$ фазовым методом, Ñредние чаÑтоты} + +Получим график завиÑимоÑти $tg(\psi)$ от $\nu$ Ð´Ð»Ñ Ñ‡Ð°Ñтот от $0.05 \nu_h$ до $0.5 \nu_h$: + +\begin{center} + \begin{tikzpicture} + \begin{axis}[ + title={График 2 \quad График завиÑимоÑти $ tg(\psi)(\nu) $}, + xlabel={$ \nu $, Гц}, + ylabel={$tg(\psi)$}, + legend pos=south east, + xmajorgrids=true, + ymajorgrids=true, + grid style=dashed, + width = 520, + height = 350, + %xmin = 300, + %xmax = 335, + %ymin =40, + %ymax =135, + ] + \legend{ + ЭкÑпериментальные данные, + Уровень "беÑконечноÑть", + ÐппрокÑÐ¸Ð¼Ð°Ñ†Ð¸Ñ Ð´Ð°Ð½Ð½Ñ‹Ñ…, + }; + \addplot [black, only marks, mark size = 2pt, + error bars/.cd, + x dir=both, x explicit, + y dir=both, y explicit, + ] table [x = T, y = sigma, y error plus = YError, y error minus = YError] { + T sigma YError + 130 1.19 0.30 + 153 1.0 0.50 + 176 1.25 0.48 + 200 1.82 0.54 + 225 1.56 0.43 + 300 1.91 0.87 + 400 2.08 0.67 + 500 -6.0 1.16 + 600 6.96 3.10 + 700 11.75 4.37 + 800 10.15 3.27 + 900 8.88 2.50 + 950 0 0 + 1000 7.92 2.0 + 1120 0 0 + }; + \addplot [red, domain=0:1120, line width =1.0pt]{0*x + 0}; + \addplot [blue, domain = 130:400, line width = 3.0pt]{0.0038*x + 0.69}; + \end{axis} + \end{tikzpicture} +\end{center} + +По разброÑу и общему качеÑтву данных можно заключить, что Ð»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ Ð°Ð¿Ð¿Ñ€Ð¾ÐºÑÐ¸Ð¼Ð°Ñ†Ð¸Ñ Ð·Ð´ÐµÑÑŒ неумеÑтна, но еÑли вÑе же Ð´Ð»Ñ Ð¾Ñ†ÐµÐ½ÐºÐ¸ допуÑтить ее Ð´Ð»Ñ Ð¿ÐµÑ€Ð²Ñ‹Ñ… 7 точек, больше вÑего напоминающих линейную завиÑимоÑть, получим: + +\begin{equation} + k = 0.0038 \pm 0.0031 +\end{equation} + +И тогда из Ñоотношений (7) и (11) получаем $\sigma$: + +\begin{equation} + \sigma = \frac{k}{ah\pi\mu_0} \approx 3.06 \pm 2.49 \cdot 10^7 \text{См/м} +\end{equation} + +\subsection{Определение $\sigma$ фазовым методом, выÑокие чаÑтоты} + +Ð”Ð»Ñ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ метода иÑпользуетÑÑ Ð´Ð¸Ð°Ð¿Ð°Ð·Ð¾Ð½ чаÑтот от 0.5 $\nu_h$ до 15 $\nu_h$, данные перечиÑлены в Ñерии таблиц ниже: + +\begin{table}[H] + \centering + \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} + \hline + $ \nu $, Гц & 1405 & 1760 & 2210 & 2775 & 3480 & 4365 & 5477 & 6870 & 8620 & 10813 \\ \hline + $ U $, Ð’ & 0.6537 & 0.5901 & 0.5175 & 0.4415 & 0.3676 & 0.2991 & 0.2380 & 0.1857 & 0.1417 & 0.1060\\ \hline + $ I $, мР& 243.1 & 219.6 & 193.2 & 166.0 & 139.7 & 115.6 & 94.32 & 76.2 & 60.85 & 47.96 \\ \hline + $ X $ & 3.4 & 2.7 & 4.3 & 3.3 & 2.5 & 1.9 & 3.5 & 2.6 & 1.9 & 2.7 \\ \hline + $ X_0 $ & 3.5 & 2.8 & 4.6 & 3.6 & 2.9 & 2.3 & 4.5 & 3.6 & 2.8 & 4.6 \\ \hline + \end{tabular} + \caption{Результаты измерений от 0.5 $\nu_h$ до 15 $\nu_h$ - 1} + \label{tab:my-table1} +\end{table} + +\begin{table}[H] + \centering + \begin{tabular}{|c|c|c|c|c|c|} + \hline + $ \nu $, Гц & 13565 & 17020 & 21350 & 26780 & 33600 \\ \hline + $ U $, Ð’ & 0.0780 & 0.057 & 0.0427 & 0.0334 & 0.0280\\ \hline + $ I $, мР& 37.05 & 27.63 & 19.25 & 11.4 & 4.02 \\ \hline + $ X $ & 1.8 & 1.2 & 1.1 & 0.7 & 0.2 \\ \hline + $ X_0 $ & 3.7 & 2.9 & 4.6 & 3.7 & 2.9 \\ \hline + \end{tabular} + \caption{Результаты измерений от 0.5 $\nu_h$ до 15 $\nu_h$ - 2} + \label{tab:my-table1} +\end{table} + +ПоÑтроим график $\psi - \frac{\pi}{4}$ от $\sqrt{\nu}$: + +\begin{center} + \begin{tikzpicture} + \begin{axis}[ + title={График 2 \quad График завиÑимоÑти $\psi(\sqrt{\nu}) $}, + xlabel={$ \sqrt{\nu} $}, + ylabel={$\frac{\psi - \frac{\pi}{4}}{\pi}$}, + legend pos=south east, + xmajorgrids=true, + ymajorgrids=true, + grid style=dashed, + width = 520, + height = 350, + %xmin = 300, + %xmax = 335, + %ymin =40, + %ymax =135, + ] + \legend{ + ЭкÑпериментальные данные, + ÐппрокÑÐ¸Ð¼Ð°Ñ†Ð¸Ñ Ð´Ð°Ð½Ð½Ñ‹Ñ…, + }; + \addplot [black, only marks, mark size = 2pt, + error bars/.cd, + x dir=both, x explicit, + y dir=both, y explicit, + ] table [x = T, y = sigma, y error plus = YError, y error minus = YError] { + T sigma YError + 37.5 0.505 0.00013 + 42.0 0.506 0.00021 + 47.0 0.511 0.00024 + 52.7 0.514 0.00040 + 59.0 0.524 0.00086 + 66.1 0.530 0.00143 + 74.0 0.540 0.00097 + 82.9 0.551 0.00161 + 92.8 0.560 0.00250 + 104.0 0.581 0.00213 + 116.5 0.606 0.00357 + 130.5 0.625 0.00549 + 146.1 0.675 0.00498 + 163.6 0.690 0.00673 + 183.3 0.728 0.01003 + }; + %\addplot [red, domain=0:1120, line width =1.0pt]{0*x + 0}; + \addplot [blue, domain = 130:190, line width = 3.0pt]{0.0019*x + 0.38}; + \end{axis} + \end{tikzpicture} +\end{center} + +ВзÑв поÑледние 4 точки Ð´Ð»Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ аппрокÑимации, получим: + +\begin{equation} + k = 0.0019 \pm 0.001 +\end{equation} + +Тогда $\sigma$ (из ÑÐ¾Ð¾Ñ‚Ð½Ð¾ÑˆÐµÐ½Ð¸Ñ (13)): + +\begin{equation} + \sigma = (\frac{k\pi}{h\sqrt{\pi \mu_0}})^2 \approx 3.61\pm 0.44 \cdot 10^7 \text{ См/м} +\end{equation} + +\subsection{Получение итоговой $\sigma$ и проверка теории об оÑлаблении полей} + +ЗанеÑем в таблицу полученные коÑффициенты проводимоÑти: + +\begin{table}[H] + \centering + \begin{tabular}{|c|c|c|c|} + \hline + $ \sigma $, $10^7$ См/м & 4.71 $\pm 0.3$ & 3.06 $\pm 2.49$ & 3.61 $\pm 0.44$ \\ \hline + â„–, ÑпоÑоб & 1 & 2 & 3 \\ \hline + \end{tabular} + \caption{Результаты раÑÑчета $\sigma$} + \label{tab:my-table1} +\end{table} + +Первый результат, еÑли Ñудить по погрешноÑти и качеÑтву аппрокÑимации теоретичеÑких положений, Ñразу выделÑетÑÑ Ð½Ð° фоне двух других. ИÑÐ¿Ð¾Ð»ÑŒÐ·ÑƒÑ Ð¿Ð¾Ð»ÑƒÑ‡ÐµÐ½Ð½Ð¾Ðµ в первом ÑпоÑобе $\xi_0$, раÑÑчитаем коÑффициент оÑÐ»Ð°Ð±Ð»ÐµÐ½Ð¸Ñ Ð¿Ð¾Ð»Ñ Ð´Ð»Ñ Ð²Ñех измерений и получим график $\frac{H_1}{H_0}$ от $\nu$: + +\begin{center} + \begin{tikzpicture} + \begin{axis}[ + title={График 2 \quad График завиÑимоÑти $\frac{H_1}{H_0}(\ln{\nu}) $}, + xlabel={$ \ln{\nu} $}, + ylabel={$\frac{H_1}{H_0}$}, + legend pos=north east, + xmajorgrids=true, + ymajorgrids=true, + grid style=dashed, + width = 520, + height = 350, + %xmin = 300, + %xmax = 335, + %ymin =40, + %ymax =135, + ] + \legend{ + ЭкÑпериментальные данные, + $\sigma$ 3 ÑпоÑоба, + $\sigma$ 1 ÑпоÑоба, + }; + \addplot [black, only marks, mark size = 2pt, + error bars/.cd, + x dir=both, x explicit, + y dir=both, y explicit, + ] table [x = T, y = sigma, y error plus = YError, y error minus = YError] { + T sigma YError + 3.1135153092103742 0.9952380952380953 0.003034528852627153 + 3.481240089335692 0.9844652734548689 0.0024296396430131192 + 3.7495040759303713 0.9712324209889613 0.0021051211301746837 + 3.912023005428146 0.9600198113207549 0.0019442412869348528 + 4.0943445622221 0.9435485413677667 0.001789457047705763 + 4.248495242049359 0.9250641470180305 0.0016747075788558427 + 4.382026634673881 0.9050400443568261 0.0015842121819330038 + 4.499809670330265 0.8839557780559033 0.0015102218517364016 + 4.605170185988092 0.8620851550584648 0.001447037944914165 + 4.700480365792417 0.8398451213216315 0.001392131263732335 + 4.867534450455582 0.7955511456628477 0.0012997583061895796 + 5.030437921392435 0.7450367814980199 0.001208201187952468 + 5.170483995038151 0.6965798903878584 0.001126721258817063 + 5.298317366548036 0.6497147786083957 0.0010513947363547955 + 5.41610040220442 0.6048946236559141 0.0009805030758504225 + 5.703782474656201 0.49464613970588234 0.0008081550853337661 + 5.991464547107982 0.3924984091632199 0.0006485268400623924 + 6.214608098422191 0.3228732090284593 0.0005398653533340845 + 6.396929655216146 0.27328343949044587 0.0004633258148795047 + 6.551080335043404 0.236407326007326 0.0004056899694526069 + 6.684611727667927 0.2081123905429072 0.00036375114094642244 + 6.802394763324311 0.18608629563135848 0.00033191735368353476 + 6.856461984594587 0.1764 0.00031801148325358845 + 6.907755278982137 0.16791591160220995 0.00030608624051972367 + 7.02108396428914 0.15027906029331883 0.0002817675292202461 + 7.247792581767846 0.12000096616801663 0.00024190589955894109 + 7.473069088032197 0.09573002049180329 0.00021257279158849482 + 7.700747794511798 0.0759938590820944 0.00019104839419083062 + 7.928406026180535 0.06009345490068383 0.00017528154640263647 + 8.15478757276852 0.04740972033668205 0.00016391666519055306 + 8.381373468273702 0.037165661898476796 0.00015496394055260034 + 8.608312784783722 0.028886702244547056 0.0001473264474642386 + 8.834919385216395 0.022241687583811846 0.00014011610005098057 + 9.061840363657739 0.016938289163379576 0.00013330211988886283 + 9.288504392945537 0.012815868089464177 0.00012762400816412683 + 9.515248225093032 0.009730925175082936 0.0001251196225478801 + 9.742144402127366 0.007599796369092505 0.00013088382154919636 + 9.96880701865677 0.006514285714285715 0.00016158951306304936 + 10.195410619245164 0.006859596713965646 0.0002906034549550167 + 10.422281345951296 0.012997512437810948 0.0015934155225007696 + }; + \addplot [red, only marks, mark size = 2pt, + error bars/.cd, + x dir=both, x explicit, + y dir=both, y explicit, + ] table [x = T, y = sigma, y error plus = YError, y error minus = YError] { + T sigma YError + 3.1135153092103742 0.991831150503086 0 + 3.481240089335692 0.9831029886272947 0 + 3.7495040759303713 0.9714401816626221 0 + 3.912023005428146 0.9608903488271511 0 + 4.0943445622221 0.9446140957470106 0 + 4.248495242049359 0.9260597298979459 0 + 4.382026634673881 0.9055162257178208 0 + 4.499809670330265 0.8832833893105745 0 + 4.605170185988092 0.859662515153242 0 + 4.700480365792417 0.8349481796578916 0 + 4.867534450455582 0.7833445793964252 0 + 5.030437921392435 0.7225401400241185 0 + 5.170483995038151 0.6624548336674982 0 + 5.298317366548036 0.6023569033450877 0 + 5.41610040220442 0.5438472296913146 0 + 5.703782474656201 0.3979377985729857 0 + 5.991464547107982 0.2658453717541181 0 + 6.214608098422191 0.1828674545309444 0 + 6.396929655216146 0.12942026929262404 0 + 6.551080335043404 0.09367955802765128 0 + 6.684611727667927 0.06887327666608066 0 + 6.802394763324311 0.05107103638557163 0 + 6.856461984594587 0.044020398682463296 0 + 6.907755278982137 0.037918507304403874 0 + 7.02108396428914 0.026255786004001226 0 + 7.247792581767846 0.009067629996455733 0 + 7.473069088032197 -0.00206736070310733 0 + 7.700747794511798 -0.009277365425469643 0 + 7.928406026180535 -0.013779952201647456 0 + 8.15478757276852 -0.016454019724793212 0 + 8.381373468273702 -0.01787514262468859 0 + 8.608312784783722 -0.018353623331252844 0 + 8.834919385216395 -0.018044279723335718 0 + 9.061840363657739 -0.017008497686647236 0 + 9.288504392945537 -0.015282934043383052 0 + 9.515248225093032 -0.012947118025423983 0 + 9.742144402127366 -0.010189944128956184 0 + 9.96880701865677 -0.00732145245861438 0 + 10.195410619245164 -0.004685032652487981 0 + 10.422281345951296 -0.002551967810460947 0 + }; + \addplot [blue, only marks, mark size = 2pt, + error bars/.cd, + x dir=both, x explicit, + y dir=both, y explicit, + ] table [x = T, y = sigma, y error plus = YError, y error minus = YError] { + T sigma YError + 3.1135153092103742 0.9808558650755765 0 + 3.481240089335692 0.960853464750505 0 + 3.7495040759303713 0.9348285317845538 0 + 3.912023005428146 0.9119524241496652 0 + 4.0943445622221 0.877839334975471 0 + 4.248495242049359 0.8406017211202917 0 + 4.382026634673881 0.8012879107875045 0 + 4.499809670330265 0.7608486722304304 0 + 4.605170185988092 0.7201051956470438 0 + 4.700480365792417 0.6797350918158642 0 + 4.867534450455582 0.6021186780806851 0 + 5.030437921392435 0.5206994183266047 0 + 5.170483995038151 0.4492123199567288 0 + 5.298317366548036 0.38521863673179535 0 + 5.41610040220442 0.3290588935655731 0 + 5.703782474656201 0.21023495609055895 0 + 5.991464547107982 0.12286114438143612 0 + 6.214608098422191 0.07552994376137419 0 + 6.396929655216146 0.0476232726858382 0 + 6.551080335043404 0.02997765091908598 0 + 6.684611727667927 0.01818188377994179 0 + 6.802394763324311 0.00993909968524122 0 + 6.856461984594587 0.006726073944593476 0 + 6.907755278982137 0.003969493107643403 0 + 7.02108396428914 -0.001234442984143465 0 + 7.247792581767846 -0.008724785457461129 0 + 7.473069088032197 -0.013402205739184585 0 + 7.700747794511798 -0.016248711509291792 0 + 7.928406026180535 -0.01778345374760842 0 + 8.15478757276852 -0.018343197685066197 0 + 8.381373468273702 -0.01810735178031715 0 + 8.608312784783722 -0.017141361016377796 0 + 8.834919385216395 -0.015481845464164564 0 + 9.061840363657739 -0.013197671142429852 0 + 9.288504392945537 -0.010472459919523723 0 + 9.515248225093032 -0.007598633966155825 0 + 9.742144402127366 -0.004922180536405742 0 + 9.96880701865677 -0.0027334646937310875 0 + 10.195410619245164 -0.0011753495288490618 0 + 10.422281345951296 -0.00024221031435657208 0 + }; + %\addplot [red, domain=0:1120, line width =1.0pt]{0*x + 0}; + + \end{axis} + \end{tikzpicture} +\end{center} + + +\section{ОбÑуждение результатов и выводы} + +Ð’ ходе работы нами было иÑпользовано три метода Ð´Ð»Ñ Ð¾Ð¿Ñ€ÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¿Ñ€Ð¾Ð²Ð¾Ð´Ð¸Ð¼Ð¾Ñти меди по Ñкин-Ñффекту, коÑвенно в ней наблюдающемÑÑ: по Ñоотношению амплитуд полей на низких чаÑтотах и по фазам на Ñредних и выÑоких чаÑтотах. Первый и третий методы показывали в ходе ÑкÑперимента хорошее качеÑтвенное Ñовпадение Ñ Ñ‚ÐµÐ¾Ñ€Ð¸ÐµÐ¹, в отличие от второго, в котором ÑÐ¸Ñ‚ÑƒÐ°Ñ†Ð¸Ñ ÐºÐ°Ñ€Ð´Ð¸Ð½Ð°Ð»ÑŒÐ½Ð¾ противоположнаÑ. ПроводимоÑть, Ð¿Ð¾Ð»ÑƒÑ‡ÐµÐ½Ð½Ð°Ñ Ð² первом методе, хорошо Ñовпадает Ñ Ñ‚Ð°Ð±Ð»Ð¸Ñ‡Ð½Ñ‹Ð¼Ð¸ значениÑми проводимоÑти меди, ÑƒÑ‡Ð¸Ñ‚Ñ‹Ð²Ð°Ñ Ð¿Ñ€Ð¸Ð¼ÐµÑи в ней, но поÑтроение графиков $\frac{H_1}{H_0}$ показало, что Ñ‚ÐµÐ¾Ñ€Ð¸Ñ Ð¾Ð¿Ð¸Ñала данные качеÑтвенно, но не количеÑтвенно. Результаты опытов, по нашему мнению, могут быть объÑÑнены Ñледующими положениÑми: + +1. ИÑпользование в качеÑтве теоретичеÑкой оÑновы упрощенного Ñ€ÐµÑˆÐµÐ½Ð¸Ñ Ñкин-Ñффекта Ð´Ð»Ñ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑ€Ð½Ð¾Ð³Ð¾ ÑÐ»ÑƒÑ‡Ð°Ñ - Ñто ведет к переоценке второй производной на выÑоких чаÑтотах и вÑледÑтвии к занижению Ð¿Ð¾Ð»Ñ Ð²Ð½ÑƒÑ‚Ñ€Ð¸ цилинлра. + +2. Предположение о ÑтационарноÑти полей может быть неккоретно на выÑоких чаÑтотах, когда характерные размеры ÑиÑтемы уже не ÑоответÑтвуют характерной ÑкороÑти раÑпроÑÑ‚Ñ€Ð°Ð½ÐµÐ½Ð¸Ñ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ в ÑиÑтеме. + +3. ÐеточноÑть Ð¾Ð¿Ñ€ÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ñ„Ð°Ð· по нулÑм напрÑжений на изм. катушке и резиÑторе, оÑобенно проÑвлÑющуюÑÑ Ð¿Ñ€Ð¸ приближении разноÑти фаз к $\pi$/2 и ÑледÑтвенно Ñовпадению фаз на оÑциллографе. + +4. КачеÑтвенное раÑхождение на Ñредних чаÑтотах может быть ÑвÑзано Ñ "переходом" Ñ€ÐµÑˆÐµÐ½Ð¸Ñ Ð¼ÐµÐ¶Ð´Ñƒ облаÑÑ‚Ñми аппрокÑимации. УчитываÑ, что "Ð¾Ð¿Ð¾Ñ€Ð½Ð°Ñ Ñ‡Ð°Ñтота" была вычиÑлена по оценке проводимоÑти, границы перехода могли быть определены неточно. + +Ð’ таких уÑловиÑÑ…, мы можем утверждать Ñледущее: Ñ‚ÐµÐ¾Ñ€Ð¸Ñ Ð² одномерном приближении опиÑывает Ð½Ð°Ð±Ð»ÑŽÐ´ÐµÐ½Ð¸Ñ ÐºÐ°Ñ‡ÐµÑтвенно, о качеÑтве количеÑтвенного опиÑÐ°Ð½Ð¸Ñ Ñудить Ñложно. + +\section{Рекоммендации по уÑтановке} + +Мы Ñчитаем нелишними Ñледующие корректировки по данной работе: + +1. ИÑпользовать альтернативный метод Ð¾Ð¿Ñ€ÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ñ€Ð°Ð·Ð½Ð¾Ñти фаз, оправдавший ÑÐµÐ±Ñ Ð² ранних работах - по фазовым диаграмам(иÑÐ¿Ð¾Ð»ÑŒÐ·ÑƒÑ Ð¾Ñциллограф в режиме одного из Ñигналов поданного на временную развертку) Ð´Ð»Ñ Ð±Ð¾Ð»ÐµÐµ выÑокой точноÑти, либо иÑпользовать Ñлектронный оÑциллограф, на котором можно крайне точно определÑть нужные величины. + +2. По первым раÑÑчетам $\sigma$ корректировать "опорную чаÑтоту" + +\end{document} \ No newline at end of file diff --git "a/3.7.1/George Stavisskii/\320\224\320\260\320\275\320\275\321\213\320\265" "b/3.7.1/George Stavisskii/\320\224\320\260\320\275\320\275\321\213\320\265" new file mode 100644 index 00000000..cabd46c3 --- /dev/null +++ "b/3.7.1/George Stavisskii/\320\224\320\260\320\275\320\275\321\213\320\265" @@ -0,0 +1,82 @@ +22.5 0.1555 435.4 +32.5 0.2207 432.5 +42.5 0.2817 427.9 +50 0.3246 424.0 +60 0.3776 418.2 +70 0.4255 412.0 +80 0.4686 405.8 +90 0.5069 399.5 +100 0.5409 393.4 +110 0.5708 387.4 +130 0.6202 376.0 +153 0.6634 364.9 +176 0.6957 355.8 +200 0.7208 347.8 +225 0.7402 341.0 +300 0.7725 326.4 +400 0.7870 314.3 +500 0.7871 305.7 +600 0.7801 298.3 +700 0.7720 292.5 +800 0.7581 285.5 +900 0.7439 278.5 +950 0.735 275.0 +1000 0.7271 271.5 +1120 0.706 263.0 +1405 0.6537 243.1 +1760 0.5901 219.6 +2210 0.5175 193.2 +2775 0.4415 166.0 +3480 0.3676 139.7 +4365 0.2991 115.6 +5477 0.2380 94.32 +6870 0.1857 76.2 +8620 0.1417 60.85 +10813 0.1060 47.96 +13565 0.0780 37.05 +17020 0.057 27.63 +21350 0.0427 19.25 +26780 0.0334 11.4 +33600 0.0280 4.02 + + +22.5 +32.5 +42.5 +50 +60 +70 +80 +90 +100 +110 +130 +153 +176 +200 +225 +300 +400 +500 +600 +700 +800 +900 +950 +1000 +1120 +1405 +1760 +2210 +2775 +3480 +4365 +5477 +6870 +8620 +10813 +13565 +17020 +21350 +26780 +33600 From 4d4e2529b771665dd4c59ddf97fb3c0a9b1eec81 Mon Sep 17 00:00:00 2001 From: StavisskiiGL <91308454+StavisskiiGL@users.noreply.github.com> Date: Fri, 14 Oct 2022 23:59:03 +0300 Subject: [PATCH 2/2] =?UTF-8?q?=D0=94=D0=BE=D0=B1=D0=B0=D0=B2=D0=B8=D0=BB?= =?UTF-8?q?=20pdf?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 3.7.1/pdf/lab371.pdf | Bin 0 -> 464184 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 3.7.1/pdf/lab371.pdf diff --git a/3.7.1/pdf/lab371.pdf b/3.7.1/pdf/lab371.pdf new file mode 100644 index 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