Experiment 4: Charge to mass ratio (e/m) of the electron # 实验4：电子的电荷质量比(e/m)

Nate Saffold

nas2173@columbia.edu Office Hour: Monday, 5:30PM-6:30PM @ Pupin 1216

INTRO TO EXPERIMENTAL PHYS-LAB 1494/2699 # 实验物理导论实验室 1494/2699

Introduction # 介绍

• Our first measurement of atomic structure
• Charge-to-mass ratio of electron:
• Motivation and history of the first $e / m$ measurement
• Consequences Thomson's experiment
• The physics behind the experiment:
• The magnetic field generated by a single loop
• Charged particle in constant magnetic field
• Measurements:
• Preliminary set-up: ambient magnetic field
• Measure charge-to-mass ratio by bending electron through constant magnetic fields
• Analysis
• 我们对原子结构的第一次测量
• 电子的电荷质量比：
• 首次 $e / m$ 测量的动机和历史
• 汤姆逊实验的后果
• 实验背后的物理学：
• 由单个环路产生的磁场
• 恒定磁场中的带电粒子
• 测量：
• 初步设置：环境磁场
• 通过恒定磁场弯曲电子来测量电荷质量比
• 分析

Why measure $e / m ?$ # 为什么测量 $e / m$ ?

• Prior to this measurement ( $\sim 1897$ ), what did we know about matter?
• ANSWER: Very little!
• We understood the classical macroscopic forces between matter:
• Gravity: $\vec{F}_{g}=-G \frac{m_{1} m_{2}}{r^{2}} \hat{r}$
• Electromagnetism:
• Maxwell's equations
• Coulomb and Lorentz forces: $\vec{F}_{e}=-k \frac{q_{1} q_{2}}{r^{2}} \hat{r} ; \vec{F}_{m}=q \vec{v} \times \vec{B}$
• Nobody really knew what the constituents of matter were. Or if there were any!
• 在这次测量之前（$\sim 1897$），我们对物质了解多少？
• 答案：非常少！
• 我们理解物质之间的经典宏观力：
• 重力：$\vec{F}_{g}=-G \frac{m_{1} m_{2}}{r^{2}} \hat{r}$
• 电磁学：
• 麦克斯韦方程组
• 库仑力和洛伦兹力：$\vec{F}_{e}=-k \frac{q_{1} q_{2}}{r^{2}} \hat{r} ; \vec{F}_{m}=q \vec{v} \times \vec{B}$
• 没有人真正知道物质的组成部分是什么。或者是否存在任何组成部分！

What is matter? # 什么是物质？

-What is matter really made of?

• Infinitely divisible (i.e. continuous matter)?
• Made up of individual constituents?
• J.J. Thomson provided experimental evidence of the existence of discrete constituents of matter:
• He showed that matter has constituents that are negatively charged and whose charge/mass ratio is constant
• This suggests that charge is not infinitely indivisible but comes in corpuscles (e.g. electrons)
• This is the first example of quantization (existence of discrete components) of nature!

-物质究竟由什么组成？

• 无限可分（即连续物质）？
• 由独立的组成部分构成？
• J.J.汤姆逊提供了物质存在离散组成部分的实验证据：
• 他表明物质有带负电荷的组成部分，且其电荷质量比是恒定的
• 这表明电荷不是无限不可分的，而是以微粒（如电子）的形式存在
• 这是自然界中量子化（离散组件的存在）的第一个例子！

Consequences # 后果

• This led Thomson to postulate the "plum pudding model":

Quanta (electrons) enclosed in a continuous positive distribution

• 这使汤姆逊提出了"布丁模型"：

量子（电子）被包含在连续的正电荷分布中

Consequences # 后果

• This led Thomson to postulate the "plum pudding model":

Quanta (electrons) enclosed in a continuous positive distribution

• Nice idea... too bad it is completely wrong...
• Rutherford scattering experiments (1911):
• Matter is made of compact localized nuclei
• Development of Quantum Mechanics (1920's):
• The microscopic constituents of matter follow novel and surprising laws of physics!
• 这使汤姆逊提出了"布丁模型"：

量子（电子）被包含在连续的正电荷分布中

• 不错的想法...可惜完全错误...
• 卢瑟福散射实验（1911）：
• 物质由紧凑的局部原子核组成
• 量子力学的发展（1920年代）：
• 物质的微观组成部分遵循新颖且令人惊讶的物理学法则！

We're not done yet! # 我们还没完成！

• Several experiments suggest that electrons might indeed be elementary, indivisible particles
• However nucleons (protons or neutrons) are not!
• 1968: Scattering experiments at the Stanford Linear ACcelerator (SLAC) show that nucleons are made of more fundamental particles: quarks
• 几个实验表明电子可能确实是基本的、不可分的粒子
• 然而核子（质子或中子）不是！
• 1968年：在斯坦福线性加速器（SLAC）进行的散射实验表明核子由更基本的粒子组成：夸克

We're not done yet! # 我们还没完成！

• Several experiments suggest that electrons might indeed be elementary, indivisible particles
• However nucleons (protons or neutrons) are not!
• 1968: Scattering experiments at the Stanford Linear Accelerator (SLAC) show that nucleons are made of more fundamental particles: quarks
• This led to the development of the Standard Model of elementary particles
• 几个实验表明电子可能确实是基本的、不可分的粒子
• 然而核子（质子或中子）不是！
• 1968年：在斯坦福线性加速器（SLAC）进行的散射实验表明核子由更基本的粒子组成：夸克
• 这导致了基本粒子的标准模型的发展

We're not done yet! # 我们还没完成！

• Several experiments suggest that electrons might indeed be elementary, indivisible particles
• However nucleons (protons or neutrons) are not!
• 1968: Scattering experiments at the Stanford Linear ACcelerator (SLAC) show that nucleons are made of more fundamental particles: quarks
• This led to the development of the Standard Model of elementary particles
• In 2012 the last piece of the puzzle completes the pictures!
• And now? What's next? late! Is it possible to go even further?
• 几个实验表明电子可能确实是基本的、不可分的粒子
• 然而核子（质子或中子）不是！
• 1968年：在斯坦福线性加速器（SLAC）进行的散射实验表明核子由更基本的粒子组成：夸克
• 这导致了基本粒子的标准模型的发展
• 2012年，拼图的最后一块完成了整个图景！
• 现在呢？接下来是什么？晚了！有可能走得更远吗？

Single loop magnetic field # 单环磁场

• Recall the Biot-Savart Law:

$$\begin{gathered} d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I d \vec{\ell} \times \hat{r}}{r^{2}} \\ \Downarrow \\ \vec{B}=\frac{\mu_{0}}{4 \pi} I \oint \frac{d \vec{\ell} \times \hat{r}}{r^{2}} \end{gathered}$$

• 回顾毕奥-萨伐尔定律：

$$\begin{gathered} d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I d \vec{\ell} \times \hat{r}}{r^{2}} \\ \Downarrow \\ \vec{B}=\frac{\mu_{0}}{4 \pi} I \oint \frac{d \vec{\ell} \times \hat{r}}{r^{2}} \end{gathered}$$

Single loop magnetic field # 单环磁场

• Recall the Biot-Savart Law:

$$\begin{gathered} d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I d \vec{\ell} \times \hat{r}}{r^{2}} \\ \Downarrow \\ \vec{B}=\frac{\mu_{0}}{4 \pi} I \oint \frac{d \vec{\ell} \times \hat{r}}{r^{2}} \end{gathered}$$

• A single ring of wire will generate a field following the right hand rule and with magnitude on the ring axis:
• 回顾毕奥-萨伐尔定律：

$$\begin{gathered} d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I d \vec{\ell} \times \hat{r}}{r^{2}} \\ \Downarrow \\ \vec{B}=\frac{\mu_{0}}{4 \pi} I \oint \frac{d \vec{\ell} \times \hat{r}}{r^{2}} \end{gathered}$$

• A single ring of wire will generate a field following the right hand rule and with magnitude on the ring axis:
• 单个线圈的导线将产生遵循右手定则的磁场，在环轴上具有特定的磁场强度：

Single loop magnetic field # 单环磁场

• Recall the Biot-Savart Law:

$$\begin{gathered} d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I d \vec{\ell} \times \hat{r}}{r^{2}} \quad \begin{array}{l} \text { Line integral } \\ \text { over the wire } \end{array} \\ \forall \vec{B}=\frac{\mu_{0}}{4 \pi} I \oint \frac{d \vec{\ell} \times \hat{r}}{r^{2}} \end{gathered}$$

• 回顾毕奥-萨伐尔定律：

$$\begin{gathered} d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I d \vec{\ell} \times \hat{r}}{r^{2}} \quad \begin{array}{l} \text { Line integral } \\ \text { over the wire } \end{array} \\ \forall \vec{B}=\frac{\mu_{0}}{4 \pi} I \oint \frac{d \vec{\ell} \times \hat{r}}{r^{2}} \end{gathered}$$

• A single ring of wire will generate a field following the right hand rule and with magnitude on the ring axis:
• 单个环形的导线将产生遵循右手定则的磁场，在环轴上具有特定的磁场强度：

Circular motion of charge in B field # 带电粒子在B场中的圆周运动

• The second ingredient we are going to use is the motion of a charge experiencing a constant magnetic field
• Last time (exp. 3) we saw that a particle of charge $q$, entering a region of space with constant $B$ field at a velocity $v$ feels a Lorentz force:

$$F=q v B$$

• Since velocity and force are perpendicular to each other the motion will be circular
• In particular, the centripetal force must be provided by the Lorentz force itself and hence:

$$q v B=m \frac{v^{2}}{r} \quad \Rightarrow \quad \frac{q}{m}=\frac{v}{r B}$$

• 我们将要使用的第二个要素是带电粒子在恒定磁场中的运动
• 上次（实验3）我们看到，电荷为$q$的粒子，以速度$v$进入具有恒定$B$场的空间区域时，会感受到洛伦兹力：

$$F=q v B$$

• 由于速度和力相互垂直，运动将是圆周的
• 特别地，向心力必须由洛伦兹力本身提供，因此：

$$q v B=m \frac{v^{2}}{r} \quad \Rightarrow \quad \frac{q}{m}=\frac{v}{r B}$$

Circular motion of charge in B field # 带电粒子在B场中的圆周运动

• However, measuring the velocity of an elementary particle is a very non-trivial business
• A simple solution to this problem is to speed the electrons up thanks to a known potential difference (e.g. generated by two plates with opposite charge)
• In this case conservation of energy tells us that:

$$q V=\frac{1}{2} m v^{2} \quad \Rightarrow \quad \frac{q}{m}=\frac{v^{2}}{2 V}$$

• Combining it with the previous result, we can eliminate the velocity from the equation:
• 然而，测量基本粒子的速度是一项非常不简单的工作
• 解决这个问题的一个简单方法是利用已知的电势差（例如由两个带相反电荷的极板产生）来加速电子
• 在这种情况下，能量守恒告诉我们：

$$q V=\frac{1}{2} m v^{2} \quad \Rightarrow \quad \frac{q}{m}=\frac{v^{2}}{2 V}$$

• 将其与前面的结果结合，我们可以从方程中消除速度：

The Experiment # 实验

Main goals # 主要目标

• The equipment:
• Helmholtz coils: provide magnetic field
• Cathode ray tube: provides electron beam
• Measuring rods: allow to measure the radius of the circular motion
• The experiment:
• Alignment of experimental apparatus with the ambient magnetic field $B_{E}$
• Preliminary measure of $B_{E}$
• Bend electron beam with magnetic field and measure $e / m$
• 设备：
• 亥姆霍兹线圈：提供磁场
• 阴极射线管：提供电子束
• 测量杆：用于测量圆周运动的半径
• 实验：
• 将实验装置与环境磁场 $B_{E}$ 进行对准
• 初步测量 $B_{E}$
• 用磁场弯曲电子束并测量 $e / m$

Apparatus # 装置

• For this experiment:
• Use two coils with current $I$
• Cathode ray tube centered in between Helmholtz coils
• 对于这个实验：
• 使用带有电流 $I$ 的两个线圈
• 阴极射线管位于亥姆霍兹线圈之间的中心

Helmholtz coils (uniform magnetic field) # 亥姆霍兹线圈（均匀磁场）

• For this experiment:
• Use two coils with current $I$
• 对于这个实验：
• 使用带有电流 $I$ 的两个线圈

Helmholtz coils (uniform magnetic field) # 亥姆霍兹线圈（均匀磁场）

• For this experiment:
• Use two coils with current $I$
• For this setup we need the magnetic field at the center of the Helmotz coils $(z=R / 2)$ :

$$\begin{aligned} B_{I} & =\frac{\mu_{0}}{4 \pi} \frac{2 \pi R^{2} N I}{\left(R^{2}+(R / 2)^{2}\right)^{3 / 2}} \\ & \equiv C I \end{aligned}$$

This represents magnetic field at center of experimental apparatus. (Location where cathode ray tube will sit)

• Calculate constant $C$ from $R$ and $N$ !
• 对于这个实验：
• 使用带有电流 $I$ 的两个线圈
• 对于这个设置，我们需要在亥姆霍兹线圈中心 $(z=R / 2)$ 处的磁场：

$$\begin{aligned} B_{I} & =\frac{\mu_{0}}{4 \pi} \frac{2 \pi R^{2} N I}{\left(R^{2}+(R / 2)^{2}\right)^{3 / 2}} \\ & \equiv C I \end{aligned}$$

这代表实验装置中心处的磁场。（阴极射线管将放置的位置）

• 从 $R$ 和 $N$ 计算常数 $C$ ！

How to manage the magnetic field # 如何管理磁场

• The power supply for coils and filament looks like:
• 线圈和灯丝的电源看起来像：

Preliminary alignment # 初步对准

• The equipment:
• Helmholtz coils: provide magnetic field
• Cathode ray tube: provides electron beam
• Measuring rods: allows to measure the radius of the circular motion
• The experiment:
• Alignment of experimental apparatus with the ambient magnetic field $B_{E}$
• Preliminary measure of $B_{E}$
• Bend electron beam with magnetic field and measure $e / m$
• 设备：
• 亥姆霍兹线圈：提供磁场
• 阴极射线管：提供电子束
• 测量杆：用于测量圆周运动的半径
• 实验：
• 将实验装置与环境磁场 $B_{E}$ 进行对准
• 初步测量 $B_{E}$
• 用磁场弯曲电子束并测量 $e / m$

Aligning to environment magnetic field # 与环境磁场对准

• Even without any current the electron will still experience the ambient magnetic field $B_{E}$ (Earth, nearby magnets, etc.)
• We want to minimize and estimate this effect
• 即使没有任何电流，电子仍然会受到环境磁场 $B_{E}$ 的影响（地球，附近的磁铁等）
• 我们想要最小化并估计这种效应

Aligning to environment magnetic field # 与环境磁场对准

• Even without any current the electron will still experience the ambient magnetic field $B_{E}$ (Earth, nearby magnets, etc.)
• We want to minimize and estimate this effect
• By rotating the Helmotz coil we can bring $B_{I}$ and $B_{E}$ parallel to each other
• Therefore:
• 即使没有任何电流，电子仍然会受到环境磁场 $B_{E}$ 的影响（地球，附近的磁铁等）
• 我们想要最小化并估计这种效应
• 通过旋转亥姆霍兹线圈，我们可以使 $B_{I}$ 和 $B_{E}$ 相互平行
• 因此：

$$B_{\mathrm{net}}=B_{I}-B_{E}$$

Aligning to environment field # 与环境磁场对准

• To fully determine the magnitude of the ambient magnetic field we need to align the experiment to $B_{E}$
• 为了完全确定环境磁场的大小，我们需要将实验与 $B_{E}$ 对准

Aligning to environment field # 与环境磁场对准

• To fully determine the magnitude of the ambient magnetic field we need to align the experiment to $B_{E}$
• Procedure: Use compass
• Place compass flat horizontally
• Rotate coils to align with $\vec{B}_{\|}$. Needle must be on 90 or 270 degrees
• 为了完全确定环境磁场的大小，我们需要将实验与 $B_{E}$ 对准
• 程序：使用指南针
• 将指南针水平放置
• 旋转线圈以与 $\vec{B}_{\|}$ 对齐。指针必须指向90或270度

Aligning to environment field # 与环境磁场对准

• To fully determine the magnitude of the ambient magnetic field we need to align the experiment to $B_{E}$
• Procedure: Use compass
• Place compass flat horizontally
• Rotate coils to align with $\vec{B}_{\|}$. Needle must be on 90 or 270 degrees
• Rotate compass vertically
• Rotate experiment to align with $\vec{B}_{\perp}$. Needle must be on 0 or 180 degrees
• Now your Helmotz coil is nicely aligned with the ambient field!
• 为了完全确定环境磁场的大小，我们需要将实验与 $B_{E}$ 对准
• 程序：使用指南针
• 将指南针水平放置
• 旋转线圈以与 $\vec{B}_{\|}$ 对齐。指针必须指向90或270度
• 垂直旋转指南针
• 旋转实验装置以与 $\vec{B}_{\perp}$ 对齐。指针必须指向0或180度
• 现在您的亥姆霍兹线圈已经很好地与环境磁场对齐！

Aligning to environment field: tips # 与环境磁场对准：提示

• Make sure to align horizontally before you align vertically.
• Reading compass needle:
• When aligning, needle will oscillate!
• Wait until compass needle has stopped oscillating (maybe help reduce the oscillations with your hand) to determine if experimental apparatus is aligned
• Tip: Wait about 30 seconds before determining if it's aligned.
• Parallax errors:
• Once again, try to be careful and consistent in eye alignment with compass needle
• This preliminary set up is really important. Once you're done ask your TA to check that everything is fine!
• 确保在垂直对齐之前先水平对齐。
• 读取指南针指针：
• 对齐时，指针会摆动！
• 等待指南针指针停止摆动（可能需要用手帮助减少摆动）以确定实验装置是否对齐
• 提示：等待约30秒再确定是否对齐。
• 视差误差：
• 再次强调，尝试在与指南针指针的眼睛对齐方面保持谨慎和一致
• 这个初步设置非常重要。完成后请让您的助教检查一切是否正常！

Aligning to environment field: tips # 与环境磁场对准：提示

• After you completed your alignment procedure the whole apparatus should look like:

Rotated to align with the vertical component of $B_{E}$

• 完成对准程序后，整个装置应该看起来像：

旋转以与 $B_{E}$ 的垂直分量对齐

Preliminary measure of $B_{E}$ # 初步测量 $B_{E}$

• The equipment:
• Helmholtz coils: provide magnetic field
• Cathode ray tube: provides electron beam
• Measuring rods: allows to measure the radius of the circular motion
• The experiment:
• Alignment of experimental apparatus with the ambient magnetic field $B_{E}$
• Preliminary measure of $B_{E}$
• Bend electron beam with magnetic field and measure $e / m$
• 设备：
• 亥姆霍兹线圈：提供磁场
• 阴极射线管：提供电子束
• 测量杆：用于测量圆周运动的半径
• 实验：
• 将实验装置与环境磁场 $B_{E}$ 进行对准
• 初步测量 $B_{E}$
• 用磁场弯曲电子束并测量 $e / m$

Adjusting voltage on heated filament # 调节加热灯丝上的电压

• Same power supply as Helmholtz coils

Voltmeter - measure voltage potential on the filament that ejects the electrons

Voltage adjust knob

Filament potential reversal

• 与亥姆霍兹线圈相同的电源

电压表 - 测量喷射电子的灯丝上的电压电位

电压调节旋钮

灯丝电位反转

Measuring the Ambient field # 测量环境磁场

• Turn Helmholtz coils off : $\vec{B}_{I}=0$
• Note that the beam will be curved
• Set the Helmholtz coil current gain setting to 200 mA
• Using the "coil reverse" switch and "current adjustment knob", determine the current needed to make the beam trajectory straight
• When the beam is straight it must be $B_{I}=B_{E}$
• Determine $B_{E}$ (with errors!)
• 关闭亥姆霍兹线圈：$\vec{B}_{I}=0$
• 注意束将是弯曲的
• 将亥姆霍兹线圈电流增益设置设为200 mA
• 使用"线圈反转"开关和"电流调节旋钮"，确定使束轨迹变直所需的电流
• 当束变直时，必须是 $B_{I}=B_{E}$
• 确定 $B_{E}$（包括误差！）

Measuring e/m # 测量 e/m

• The equipment:
• Helmholtz coils: provide magnetic field
• Cathode ray tube: provides electron beam
• Measuring rods: allows to measure the radius of the circular motion
• The experiment:
• Alignment of experimental apparatus with the ambient magnetic field $B_{E}$
• Preliminary measure of $B_{E}$
• Bend electron beam with magnetic field and measure $e / m$
• 设备：
• 亥姆霍兹线圈：提供磁场
• 阴极射线管：提供电子束
• 测量杆：用于测量圆周运动的半径
• 实验：
• 将实验装置与环境磁场 $B_{E}$ 进行对准
• 初步测量 $B_{E}$
• 用磁场弯曲电子束并测量 $e / m$

Measuring circular orbits # 测量圆形轨道

• Turn Helmholtz coils on and set the gain switch to 10A sensitivity
• Set the filament voltage to 40 V (i.e. set the energy of the electrons)
• 打开亥姆霍兹线圈并将增益开关设置为10A灵敏度
• 将灯丝电压设置为40 V（即设置电子的能量）

Measuring circular orbits # 测量圆形轨道

• Turn Helmholtz coils on and set the gain switch to 10A setting
• Set the filament voltage to 40 V (i.e. set the energy of the electrons)
• Adjust the coil current to change radius of curvature
• 打开亥姆霍兹线圈并将增益开关设置为10A设置
• 将灯丝电压设置为40 V（即设置电子的能量）
• 调整线圈电流以改变曲率的半径

Measuring circular orbits # 测量圆形轨道

• Measure the coil current ( I ) needed to reach each bar with a fixed filament voltage $\mathrm{V}=40 \mathrm{~V}$
• The radius for each bar is given in the lab manual
• Recording uncertainties for coil current:
• Try to reduce parallax: Keep eye alignment consistent when reading ammeter and voltmeter.
• Electron current has a considerable width. Uncertainty in coil current should be done by finding maximum and minimum current as you scan the width of the beam at a given radius.
• Be consistent with where you call reference radius of the bar. (i.e. let inner radius of bar be reference radius)
• Repeat measurements for different filament voltages: 20V, $60 \mathrm{~V}, 70 \mathrm{~V}, 80 \mathrm{~V}, 100 \mathrm{~V}$
• 测量达到每个杆所需的线圈电流（I），固定灯丝电压为 $\mathrm{V}=40 \mathrm{~V}$
• 每个杆的半径在实验手册中给出
• 记录线圈电流的不确定性：
• 尝试减少视差：在读取电流表和电压表时保持眼睛对准一致。
• 电子电流有相当大的宽度。线圈电流的不确定性应通过在给定半径处扫描束的宽度来找到最大和最小电流。
• 在确定杆的参考半径时保持一致。（即让杆的内半径作为参考半径）
• 对不同的灯丝电压重复测量：20V、$60 \mathrm{~V}、70 \mathrm{~V}、80 \mathrm{~V}、100 \mathrm{~V}$

Analysis # 分析

Linearize the data by plotting / vs. 1/r

• According to what explained in the previous slides:

$$I=\left(\frac{1}{C} \sqrt{\frac{2 V}{e / m}}\right) \frac{1}{r}+\left(\frac{B_{E}}{C}\right)$$

• Perform a linear (weighted!) fit and find slope and intercept
• Compare the value obtained for $\underline{e} / m$ and the ambient field with:
• The accepted: $(\mathrm{e} / \mathrm{m})_{\text {acc }}=1.759 \times 10^{11} \mathrm{C} / \mathrm{kg}$
• The value of $B_{E}$ measured in the preliminary part

通过绘制 / vs. 1/r 线性化数据

• 根据前面幻灯片中解释的内容：

$$I=\left(\frac{1}{C} \sqrt{\frac{2 V}{e / m}}\right) \frac{1}{r}+\left(\frac{B_{E}}{C}\right)$$

• 执行线性（加权！）拟合并找出斜率和截距
• 将获得的 $\underline{e} / m$ 和环境磁场的值与以下进行比较：
• 公认值：$(\mathrm{e} / \mathrm{m})_{\text {acc }}=1.759 \times 10^{11} \mathrm{C} / \mathrm{kg}$
• 在初步部分测量的 $B_{E}$ 的值

Final tips # 最终提示

• The hardest part of the experiment is definitely to determined $B_{E}$ with the method explained in part 2: try to determine what uncertainty you have on this part accurately! It probably will be fairly large
• Most of the procedures are two-people jobs. The best solution is probably to have someone turning the knobs and someone else looking at the apparatus
• Be very careful when handling the structure! Always move the instrument using the wooden part, not the coils neither the central bulb
• 实验最难的部分无疑是用第2部分解释的方法来确定 $B_{E}$：试图准确确定这部分的不确定性！它可能会相当大
• 大多数程序都是两个人的工作。最好的解决方案可能是让一个人转动旋钮，另一个人观察仪器
• 处理结构时要非常小心！始终使用木质部分移动仪器，而不是线圈或中央灯泡