Name: b-h curves and inductor core limits
Uploaded: 2023-04-30T06:42:59.000Z
Duration: 10 min 41 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS+Phy.P2

HS+Phy.P2U1.1

Characterization of Magnetic Components

1. 相对渗透率测定
按照以下步骤测定小型电感器（黄色/白色铁氧体磁芯）的相对磁导率。磁芯的尺寸如图2所示，线圈匝数为N=75。
<ol>
	<li>使用LCR表在120 Hz和1000 Hz两个频率下测量电感器的电感值。</li>
	<li>在面包板上搭建图1所示电路，但暂不将函数发生器输出连接至面包板。</li>
	<li>检查差分电压探头和电流探头是否存在偏移，其中电流探头连接至通道1，电压探头连接至通道2。</li>
	<li>记录差分探头本身及其在示波器上的比例系数。将差分探头设置为1/20，以获得更高的分辨率。</li>
	<li>将电流探头本身设置为100 mV/A，示波器通道设置为1X。请注意，这些比例系数在进行计算时必须使用。</li>
	<li>将函数发生器输出（50 Ω BNC输出接口）设置为峰值10 V、频率1000 Hz的正弦波形。使用差分电压探头观察波形。</li>
	<li>即使断开连接，也保持函数发生器处于开启状态，避免短接其输出端子。关闭函数发生器将重置多个设置。</li>
	<li>连接电流探头和电压探头，用于测量vC和i。</li>
	<li>检查电路是否符合预期，且所有连接均保持良好。</li>
	<li>将函数发生器连接至电路。</li>
	<li>截取测量得到的电流和电压波形图，图中至少显示三个完整周期，并包含所测信号的峰值或有效值（RMS）。</li>
	<li>在示波器的“Display”菜单中，将显示格式从“YT”更改为“XY”。</li>
	<li>通过调节通道1和通道2的垂直调节旋钮，观察B-H曲线，使其完整显示在示波器屏幕上。</li>
	<li>为获得更稳定的曲线，可在显示菜单中启用“persist”功能，设置为1或2秒。</li>
	<li>截取测量得到的B-H曲线图像。</li>
	<li>调节函数发生器频率至120 Hz，并根据需要调整曲线显示参数后，重新截取B-H曲线图像。</li>
	<li>断开函数发生器连接，并移除电感器。其余电路部分保持不变。</li>
</ol>
<img alt="环形环示意图，尺寸标注：D&lt;sub&gt;in&lt;/sub&gt;=0.85cm，D&lt;sub&gt;out&lt;/sub&gt;=1.85cm，h=0.5cm。" src="/files/ftp_upload/10164/10164fig2.jpg" data-altupdatedat="1761830439000" data-alt="图 2"> 
图 2：较小电感器磁芯的尺寸示意图。<a href="//cloudfront.jove.com/files/ftp_upload/10164/10164fig2large.jpg" target="_blank">请点击此处查看此图的放大版本。</a>
2. 确定圈数
较大的黑色电感器（Bourns 1140-472K-RC）匝数未知。为简化计算，假设其磁芯为全空气磁芯的螺线管，半径为 1.5 cm，长度为 2.5 cm。如果不采用此假设，则必须考虑磁芯的几何结构，从而使计算复杂化。然而，该假设仍然合理，因为在螺线管中，磁通必须穿过器件两侧的空气，而空气是磁通路径中的主要介质。
<ol>
	<li>使用LCR电桥，在120 Hz和1000 Hz两个频率下测量所提供电感器的电感值。</li>
	<li>将电感器接入图1所示电路中，该电路应仍保持上一实验部分的连接状态。</li>
	<li>检查差分电压探头和电流探头是否存在偏移，其中电流探头连接至通道1，电压探头连接至通道2。</li>
	<li>记录差分探头本身及其在示波器上的缩放系数。将差分探头设置为1/20，以获得更高的分辨率。</li>
	<li>将电流探头本身设置为100 mV/A，示波器通道设置为1X。请记住，在后续分析中使用任何测量值或数据采集结果进行计算时，必须应用这些缩放系数。</li>
	<li>将函数发生器输出（50 Ω BNC输出接口）设置为10 V峰值、1000 Hz正弦波形。使用差分电压探头观察波形。</li>
	<li>即使断开连接，也请保持函数发生器开启状态，但避免将其端子短路。关闭函数发生器将重置多项设置。</li>
	<li>连接电流探头和电压探头，用于测量vC和i。</li>
	<li>检查电路，确保所有连接符合预期。</li>
	<li>将函数发生器连接至电路。</li>
	<li>截取所测得电流和电压波形的屏幕图像，图像中应至少显示三个完整周期，并包含所测信号的峰值或有效值（RMS）。</li>
	<li>在示波器的“display”菜单中，将显示格式从“YT”更改为“XY”。</li>
	<li>通过调节通道1和通道2的垂直调节旋钮，观察B-H曲线，直至曲线适配示波器屏幕显示范围。</li>
	<li>为获得更稳定的曲线显示，可在显示菜单中启用“persist”功能，设置时间为1或2秒。</li>
	<li>截取所测B-H曲线的屏幕图像。</li>
	<li>调节函数发生器频率至120 Hz，并根据需要调整曲线显示设置后，重新截取B-H曲线的屏幕图像。</li>
	<li>关闭函数发生器，并拆解电路。</li>
</ol>
3. 60 Hz 变压器的 B-H 曲线
本实验中使用的变压器将115 V RMS降至24 V RMS，但仅可用于本实验的B-H曲线表征，因此仅使用120 V RMS端子。变压器的尺寸如图3所示。
<ol>
	<li>使用LCR电桥，在120 Hz（接近额定的60 Hz）下测量115 V侧绕组的电感。</li>
	<li>确保三相断路开关处于断开位置。</li>
	<li>将三相电缆连接至可变交流变压器（VARIAC）。</li>
	<li>搭建图4所示电路。将变压器放置在原型板侧面。使用香蕉电缆将可变交流变压器的AC1和N端连接至原型板。</li>
	<li>确保可变交流变压器设置在0%位置。</li>
	<li>检查差分电压探头和电流探头是否存在偏移，其中电流探头连接至通道1，电压探头连接至通道2。</li>
	<li>记录差分探头本身及其在示波器上的缩放系数。将差分探头的缩放比设置为1/200。</li>
	<li>将电流探头本身设置为100 mV/A，示波器通道设置为1X。请记住，计算时需使用这些缩放系数。</li>
	<li>连接电流探头和电压探头以测量vC和i。</li>
	<li>检查电路连接。</li>
	<li>闭合三相断路开关，并缓慢调节可变交流变压器，直至达到90%输出。</li>
	<li>截取所测电流和电压波形图，至少显示三个周期，并包含所测信号的峰值或有效值（RMS）。</li>
	<li>在示波器的“Display”菜单中，将显示格式从“YT”更改为“XY”。</li>
	<li>通过调节通道1和通道2的垂直调节旋钮，观察B-H曲线，使曲线完整显示在示波器屏幕上。</li>
	<li>为获得更稳定的曲线，可在显示菜单中启用“persist”功能，设置为1或2秒。</li>
	<li>截取所测B-H曲线的图像。</li>
	<li>将可变交流变压器恢复至0%，断开断路开关，并拆解电路。</li>
</ol>
<img alt="长方体示意图，标注尺寸 X=6.3cm，Y=5.6cm，Z=3.1cm，W=1.25cm。" src="/files/ftp_upload/10164/10164fig3.jpg" data-altupdatedat="1761830439000" data-alt="图3"> 
图3：变压器铁芯的尺寸。 <a href="//cloudfront.jove.com/files/ftp_upload/10164/10164fig3large.jpg" target="_blank">请点击此处查看此图的放大版本。</a>
<img alt="带有可变变压器、电阻器、电容器和交流分析设置的三相静态平衡电路图。" src="/files/ftp_upload/10164/10164fig4.jpg" data-altupdatedat="1761830439000" data-alt="图 4"> 
图 4：用于测定 60 Hz 变压器 B-H 曲线的测试电路。 <a href="//cloudfront.jove.com/files/ftp_upload/10164/10164fig4large.jpg" target="_blank">请点击此处查看此图的放大版本。</a>

尽管电感器和其他电磁器件（例如，变压器）在许多电气、电子和机械系统中非常常见，但为特定应用购买合适的电感器并非易事。即使购买了电感器，其数据手册中的信息也可能在实际材料、匝数和其他细节方面存在模糊之处。本实验中的测试对于计划自行制作电感器或表征现成电感器的工程师和技术人员尤为有用。这在电力电子应用（例如，DC/DC变换器）以及电机驱动应用（例如，交流滤波电感器）中十分常见，因为在这些场合中，人们往往需要更全面地了解手头电感器的特性。

磁性组分的表征

来源：Ali Bazzi，康涅狄格大学电气工程系，美国康涅狄格州斯托尔斯。
本实验的目的是从设计和材料角度，获得关于不同磁性元件的实践经验。本实验涵盖磁性材料的B-H曲线以及通过识别未知设计参数来设计电感器。电感器或变压器等磁性元件的B-H曲线，是构成其线圈绕制磁芯的磁性材料本身的特性。该特性提供了磁芯在绕组电流作用下所能承受的磁通密度信息。同时，它还揭示了磁芯在达到磁饱和前的极限状态，即当继续增大线圈电流时，磁通不再进一步增加的情况。

为了确定岩心材料的相对磁导率，可以采用两种方法。第一种方法是使用LCR表，测量用已知匝数（N）绕制的线圈的电感（L），然后按下式计算相对磁导率：
磁芯的磁阻：<img alt="静态平衡的数学公式：ℜ = N²/L。" src="/files/ftp_upload/10164/10164eq7v2.jpg" data-altupdatedat="1761830439000" data-alt="方程 7">（7）
因此，相对磁导率（µr）为：
<img alt="磁导率公式，μr=l/ℜAμo，用于磁学研究的方程。" src="/file...

来源：Ali Bazzi，康涅狄格大学电气工程系，美国康涅狄格州斯托尔斯市。  
本实验的目的是通过实践操作……

电感器或变压器等磁性元件具有由线圈内部磁芯材料决定的特性。当电流流过电感器或变压器线圈时，会产生磁场。磁芯材料维持磁场的能力，即其磁导率，决定了磁场的强度，该强度称为磁化力。磁化力进而在电感器磁芯中产生磁通量。在电感器和变压器中，磁化力与磁通密度之间的关系被定义为通过横截面积的磁通量，可通过B-H曲线进行分析。B-H曲线描述了磁芯材料的特性，并标示出其磁饱和极限。当线圈中电流继续增加而磁通量不再增加时，即达到磁饱和。本视频演示了电感器和变压器B-H曲线的测量方法，以及磁芯材料和电感线圈的表征过程。B-H 曲线展示了磁通密度 B 与磁场强度 H 之间的关系。最初，随着磁场强度的增加，磁通密度也随之增加，直至达到某一最大值。在此点之后，磁场强度的进一步增加不会引起磁通密度的显著增加，此时材料被认为已达到磁饱和。实际的磁性材料在交替施加正向和负向磁场时会表现出磁滞现象。这意味着当磁场强度降低至零时，材料中仍会保留一定的残余磁性。B-H 曲线所包围的面积与材料在正负方向磁化过程中的能量损耗成正比。由于这一特性，磁滞损耗较低的材料（如钢）通常被用于变压器铁芯。B-H 曲线还可用于描述材料的磁导率，该值计算为磁通密度与磁场强度的比值。磁导率通常与真空磁导率相关，因此被称为相对磁导率。磁化率极低的材料（如木材）具有较低的相对磁导率，而磁化率较高的材料（如铁）则具有较高的相对磁导率。为了绘制 B-H 曲线，首先必须确定磁通密度 B。为此，需测量磁通量随时间的变化率，该值可通过法拉第电磁感应定律与线圈两端的电压相关联。这一电压可通过一个与线圈并联的简单 RC 电路进行测量。有关这些计算的更多详细信息，请参阅文本版实验方案。磁场强度 H 可通过安培环路定律以及可测量的变量——线圈中的电流、线圈匝数和铁芯的平均长度——来确定。材料的 B-H 曲线可通过测量电流以及元件两端电压对时间的积分来估算。当元件的匝数和几何尺寸已知时，这些测量值可换算为实际物理量。接下来，我们将演示如何测量相对磁导率并计算 B-H 曲线。在这些实验中，将测量三个磁性元件：一个带铁氧体磁芯的小型电感器、一个匝数未知的较大黑色电感器，以及一个60 Hz变压器。首先使用尺寸如图所示、绕组匝数为75的小型电感器进行实验。第一步，使用LCR表在120 Hz和1,000 Hz下测量该电感器的电感值。第二步，按照图示搭建电路，保持函数发生器输出阻抗为50欧姆，并断开BNC连接线。接下来，连接差分电压探头和电流探头，并确认无任何偏移。将差分探头设置为120分之一档位以获得更好的分辨率。最后，将电流探头设置为100毫伏每安培（探头端），示波器端设置为1x，并记录这些缩放系数以供后续计算使用。将函数发生器输出设置为频率1,000 Hz、峰值10伏的正弦波形。测量VC和I，连接函数发生器，并确认所有电路连接均如图所示。然后，记录测得的电流和电压值。最后，将示波器显示格式从yt模式切换至xy模式，以显示B-H曲线。调节通道一和通道二的垂直调节旋钮，使曲线适配屏幕显示范围。接着，通过设置显示持久（persist）选项来稳定曲线。然后，截取该曲线的屏幕图像。最后，调整函数发生器频率至120 Hz，并根据需要重新调整曲线设置后再次截取B-H曲线的屏幕图像。最终，断开函数发生器并移除电感器，其余电路部分保持不变。为了确定较大电感器的匝数，首先测量其B-H曲线。为简化计算，假设磁芯为纯空气磁芯。首先，使用LCR表在120 Hz和1,000 Hz下测量电感器的电感值。然后，将电感器接入RC电路。采用与小电感器相同的测量步骤，测量较大电感器的B-H曲线。观察并记录测得的电流和电压。显示B-H曲线。将函数发生器的频率调节至120 Hz，并根据需要调整曲线设置。单相变压器由两个通过磁芯耦合的绕组构成。此处测量60 Hz变压器的B-H曲线。使用LCR电桥，在120 Hz条件下测量115伏侧绕组的电感。然后，使用香蕉电缆将自耦变压器的AC1和N端通过面包板电路连接到变压器的初级侧。按照之前所述调整缩放因子和函数发生器参数。将自耦变压器调至90%输出，测量电流和电压。随后显示并记录B-H曲线。如果已知线圈的匝数、平均磁芯长度和横截面积，则可直接测量线圈的电感，并据此计算相对磁导率。或者，可通过测量得到的 B-H 曲线来确定元件的相对磁导率，进而计算线圈的匝数。在 B-H 曲线的线性区域内，相对磁导率可由曲线斜率求得。利用相对磁导率，并在已知电感和磁芯尺寸的情况下，可通过以下关系式轻松计算出线圈匝数。电感器和其他电磁器件（如变压器）在许多电气、电子和机械系统中十分常见。电网通过输电线路远距离输送高压电，从而向用户供电。在长距离输电中需要采用高电压，以补偿能量损耗。沿输电线路设置的变压器可将较高的输电电压降低至配电站在以及终端用户供电所需的较低电压水平。变压器通过电磁感应实现能量传递，从而实现对交流电压的可控降压。由于钢具有较高的磁饱和点，变压器通常采用钢制铁芯。定子磁体在转子中感应出旋转磁场，使转子旋转。实际上，定子相当于变压器的初级绕组，而鼠笼结构则相当于次级绕组。交流感应电动机被广泛应用于多种场合。该电机由外部静止的绕线磁体和内部转子的铁磁芯组成。通常，转子由呈圆柱形排列的导电杆构成鼠笼结构。您刚刚观看了 JoVE 关于磁性元件表征的简介。您现在应该了解如何测量电感器和变压器的 B-H 曲线，同时确定未知的设计参数，例如相对磁导率和匝数。感谢观看。

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电气工程

磁性元件的特性

b-h curves and inductor core limits

Magnetic components such as inductors and transformers depend on the core material around their windings. In this experiment, students get hands-on experience with these parts from both a design view and a material view.

The work focuses on B-H curves, which show the magnetic behavior of a material. A B-H curve describes the magnetic flux density the core can support as current flows through the windings. It also helps show the limit before magnetic saturation occurs.

Magnetic saturation means that adding more current to the coil no longer produces more magnetic flux in the core. The experiment also includes inductor design. Students identify unknown design factors by studying the magnetic component and its material response.

B-H Curves and Inductor Core Limits

electrical safety precautions and basic equipment

electrical-safety-precautions-and-basic-equipment

Safe Handling of High-Voltage Lab Power

Safe handling of high-voltage lab power is essential in electric machine and power electronics experiments. These labs involve electrical currents, voltages, power, and energy that require extreme care. The systems used in this work can include three-phase AC voltage at 208 V, 230 V, or 480 V. They may also use up to 250 V DC and currents that can reach 10 A. These levels can be dangerous if handled without proper attention. Electrocution can happen when electricity passes through the body.

characterization of magnetic components

Magnetic components such as inductors and transformers depend on the core material around their windings. In this experiment, students get hands-on experience with these parts from both a design view and a material view. The work focuses on B-H curves, which show the magnetic behavior of a material. A B-H curve describes the magnetic flux density the core can support as current flows through the windings. It also helps show the limit before magnetic saturation occurs. Magnetic saturation...

introduction to the power pole board

Power Pole Board for DC/DC Converter Labs

The HiRel Power Pole Board is a flexible tool for studying DC/DC converters. A DC/DC converter changes direct-current voltage and current from one level to another. In many cases, voltage conversion is the main goal. This board supports several converter types on one platform. It can be used to examine boost converters, which step voltage up, and buck converters, which step voltage down. It also helps students study buck-boost converters, which can step voltage up or down. The board is also...

dc/dc boost converter

Stepping Up DC Voltage with Boost Converters

DC voltage can be increased with a boost converter. This step-up circuit is useful in many applications where a DC source must be raised without first converting it to AC, using a transformer, and then rectifying the transformer output. A boost converter uses an inductor as an energy storage device. The inductor supports the output with extra energy in addition to the DC input source. That added energy raises the output voltage. This experiment studies several characteristics of a boost...

dc/dc buck converter

Buck Converter Step-Down DC Voltage

A DC/DC buck converter steps down DC voltage in an efficient, regulated way. Unlike transformers, which easily raise or lower AC voltage and current, DC systems need switching power converters to change voltage levels. The buck converter works by chopping the input DC voltage with a series input switch. An L-C low-pass filter then smooths the chopped signal and extracts the average output voltage. A diode gives the inductor current a path when the switch is off during part of the switching...

flyback converter

Flyback Converter Voltage Step-Up and Step-Down

A flyback converter is a buck-boost converter that can both step voltage up and step it down. It also provides electrical isolation between the input and the output by using a coupled inductor, or flyback transformer. The coupled inductor acts like a transformer with a turns ratio, but it also stores energy through the air gap. This setup gives the converter both voltage step-up and step-down capability. In the experiment, the converter is studied in open-loop operation with a manually set...

single phase transformers

Single Phase Transformer Testing

Single-phase transformers step up or step down AC voltage in electric power systems. They are stationary electric machines with primary and secondary coils, also called windings. The primary winding receives the applied voltage, and the secondary winding delivers the changed voltage. Inside the transformer, current in one winding creates magnetic flux in the core. This flux links the two windings and transfers energy between them. With AC current, the changing flux induces voltage in the...

single phase rectifiers

AC to DC Conversion with Rectifiers

Rectifiers convert AC power into DC power for electronic circuits. A DC power supply provides unidirectional voltage and current. Batteries can do this, but they are limited by lifetime and cost. Using a rectifier is another way to turn AC line power into DC power. A rectifier is a device that lets current pass in one direction and blocks it in the other. It works after a forward voltage threshold is reached. Rectifiers may use a diode, a silicon controlled rectifier, or other silicon P-N...

thyristor rectifier

Controlling SCR Half-Wave Rectification

Thyristors, also called silicon controlled rectifiers (SCRs), are used to control current in a rectifier circuit. Like diodes, they let current pass from the anode to the cathode and block current in the opposite direction. Unlike a diode, a thyristor can be turned on with a gate terminal that receives a small current pulse. A thyristor is a four-layer device with alternating n-type and p-type layers. These layers form a PNPN structure with three junctions. The device has three terminals. The...

single phase inverter

DC to AC Conversion with Half-Bridge Inverters

DC to AC conversion is the main idea behind a power inverter. DC power flows in one direction, while AC current changes direction at about 50-60 Hz. Many electronic devices are designed to run on AC power, so a DC source must be inverted before it can be used with them. An inverter makes this change through switching action. The switches repeatedly flip the polarity of the input DC source at the output, or load side, for part of a switching period. A typical power inverter needs a stable DC...

dc motors

DC Motors and Generator Action

DC machines use direct current and direct voltage to create motion or generate electricity. They were the first machines of this kind to be invented. A DC machine works with two magnetic fields that are controlled by DC currents, and the same machine can be set up as either a motor or a generator when the right field excitation is available. In a DC machine, the field is usually on the stator side and the armature is on the rotor side. That arrangement is the reverse of what is found in many...

ac induction motor characterization

Three-Phase Motor Equivalent Circuit Tests

Three-phase induction motor testing can be used to find equivalent circuit parameters. The experiment uses the per-phase equivalent circuit to model the motor. This model keeps the important behavior of the original system and makes calculations easier. The procedure uses tests similar to those used in transformer characterization. These measurements help estimate the motor's circuit values from its electrical response. The experiment also aims to operate the motor in the linear torque-speed...

vfd-fed ac induction machine

Variable Frequency Drive Speed Control

Variable frequency drives, or VFDs, control the speed of AC induction motors. They are a type of adjustable speed drive and are becoming standard equipment for powering most AC induction motors. In industrial and automation settings, VFDs can provide strong control of motor speed, torque, or position. This experiment focuses on speed control with open-loop operation. It uses constant voltage-to-frequency ratio control, also called V/f control. The motor usually operates at a rated stator flux,...

ac synchronous machine synchronization

Grid Connection of AC Synchronous Generators

AC synchronous generators are a major source of electrical power worldwide. They are three-phase, wound-rotor machines that are used in many power plants. These generators need a prime mover and an exciter to produce power. A prime mover is the device that spins the generator, often a turbine driven by fluid. That fluid can come from water flowing from a dam through a long nozzle or from steam made by burning coal. Most power plants use synchronous generators, including coal, nuclear, natural...

ac synchronous machine characterization

Three-Phase Synchronous Motor Starting and V-Curves

Three-phase synchronous motors and generators are important AC machines. Wound-rotor synchronous motors are less common than permanent magnet rotor synchronous motors because the rotor field uses brushes. Synchronous generators are much more common. They are used in most existing power plants because they provide excellent frequency and voltage regulation. A synchronous motor runs at the same speed as the stator magnetic field. This gives it almost 0% speed regulation, so the rotor speed stays...

electrical engineering

本系列从电气安全视频开始, 介绍了电气实验室中常用设备的最佳实践。随后的视频介绍了电感器、变压器、变流器、整流器和逆变器等元素。

Explore B-H curves, magnetic saturation, and inductor design as students study how core materials affect inductors and transformers in this hands-on experiment.

B-H Curves and Inductor Core Limits | JoVE K12

Ali Bazzi

Overview

Principles of Magnetic Component Characterization

Measuring Relative Permeability

Identifying the Number of Turns

B-H Curve of a 60 Hz Transformer

Representative Results

Applications

Summary

Electrical Safety Precautions and Basic Equipment

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT.
Electric machines and power electronics experiments ...

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT.
The objective of this experiment is to achieve hands-on ...

Magnetic Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
Magnetic fields can be ...

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on ...

Solenoids

A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field for a solenoid is the ...

Induction

An emf is induced when the magnetic field in a coil is changed by pushing a bar magnet into or out of the coil. emfs of opposite signs are produced by ...

Faraday's Law

Faraday&#39;s law state that the induced emf is the negative change in the magnetic flux per unit of time. Any change in the magnetic field or change in ...

Lenz's Law

The direction in which the induced emf drives the current around a wire loop can be found through the negative sign. However, it is usually easier to ...

Electric Generator: Alternator

Electric generators induce an emf by rotating a coil in a magnetic field. A simple alternator is an AC generator that creates electrical energy that ...

Magnetic Field due to Moving Charges

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a ...

Magnetic Field of a Solenoid

A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field due to a solenoid is ...

Magnetic Flux

The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). ...

Magnetic Force

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a ...

DC Generator

An alternator converts mechanical energy into electrical energy that varies sinusoidally, resulting in AC current. Meanwhile, a DC generator converts ...

Plan and carry out investigations to design, build, and refine a device that works within given constraints to demonstrate that an electric current can produce a magnetic field and that a changing magnetic field can produce an electric current.

B-H Curves and Inductor Core Limits

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