📚 Experimental Investigation of Magnetic Fields | 磁场实验探究
Magnetic fields are fundamental to many physical phenomena, from the deflection of charged particles to the operation of electric motors and generators. A-level physics students are expected not only to understand the theoretical principles but also to be able to design, carry out, and evaluate experiments that explore magnetic fields. This article walks you through the key experimental investigations required for the OxfordAQA International A-Level Physics specification, covering techniques to measure magnetic flux density, explore the force on a current-carrying conductor, and investigate electromagnetic induction. We will examine the equipment, methods, analysis of results, sources of error, and safety precautions for each experiment.
磁场是许多物理现象的基础，从带电粒子的偏转到电动机和发电机的运行都离不开它。A-level 物理学生不仅要理解理论原理，还需要能够设计、实施和评估探索磁场的实验。本文带你梳理 OxfordAQA 国际 A-level 物理大纲要求的关键实验研究，涵盖测量磁通密度、探究载流导体受力以及研究电磁感应的方法。我们将详细分析每个实验的器材、方法、结果分析、误差来源和安全注意事项。
1. The Force on a Current-Carrying Wire: F = BIL | 载流导线受力：F = BIL
dicular to the field lines. The wire experiences a force F = BIL sin θ, where B is the magnetic flux density, I is the current, L is the length of wire inside the field, and θ is the angle between the wire and the field. When θ = 90°, the force simplifies to F = BIL. This relationship can be verified using a current balance, also known as an electromagnetic balance or a pivoted ‘ t passes through the rod, it experiences a magnetic force that either lifts or presses down on the rod. By adjusting the current until the rod returns to its original position, the magnetic force is balanced against the weight, allowing B to be calculated.
磁场基础实验是将一段直的载流导线垂直于磁感线放入匀强磁场中。导线受到的力为 F = BIL sin θ，其中 B 为磁通密度，I 为电流，L 是导线在磁场中的长度，θ 是导线与磁场的夹角。当 θ = 90° 时，力简化为 F = BIL。这一关系可以使用电流天平（也称电磁天平或可转动“导线摆”装置）来验证。将金属棒或硬导线放在磁场中的两条平行导轨上，棒上悬挂已知质量的重物。当电流通过金属棒时，它会受到磁力作用而抬起或下压。通过调节电流使金属棒回到原位，磁力就与重力平衡，从而可以计算出 B。
To set up the experiment, you need an electronic balance or a sensitive pivot apparatus, a pair of slab magnets (or a horseshoe magnet with large pole pieces to create an approximately uniform field), a DC power supply, an ammeter, a rheostat, and a ruler. First, measure the length of the conductor that lies within the magnetic field. This is crucial because only the portion of the wire cutting the field lines experiences the force. Place the magnets so that the field is horizontal, and orient the wire at right angles to it. Zero the balance or note the equilibrium position. Then pass a known current through the wire and measure the change in weight or the additional mass needed to rebalance. Plotting the magnetic force (weight difference) against current yields a straight line through the origin, with gradient equal to BL. If L is known, B can be determined. For greater accuracy, take multiple readings at different currents and repeat the measurement three times.
搭建此实验时，你需要电子天平或灵敏的转轴装置、一对扁平磁铁（或具有大极靴的马蹄形磁铁以产生近似均匀的磁场）、直流电源、电流表、变阻器和尺子。首先测量处于磁场中的导体长度，这至关重要，因为只有切割磁感线的导线部分才受力。放置磁铁使磁场水平，并使导线与之垂直。将天平调零或记录平衡位置。然后通入已知电流，测量重量的变化或重新平衡所需添加的质量。以磁力（重量差）对电流作图得到过原点的直线，斜率等于 BL。若 L 已知，即可求出 B。为获得更高精度，应在不同电流下多次读数，并重复测量三次。
2. Using a Hall Probe to Measure Magnetic Flux Density | 用霍尔探头测量磁通密度
A Hall probe is a semiconductor device that gives a direct voltage output proportional to the magnetic field component perpendicular to its sensing face. When a constant current flows through the probe, the charge carriers experience a magnetic force, leading to a build-up of charge on one side, creating a Hall voltage VH. This voltage is directly proportional to B. Hall probes are calibrated by the manufacturer, but they can also be checked in a known magnetic field. In the lab, a Hall probe is used to map the field between the poles of a magnet, investigate the uniformity of the field, and measure B at specific points. For a permanent magnet, the probe is placed at the centre of the gap and rotated to find the maximum reading, which corresponds to the perpendicular field component.
霍尔探头是一种半导体器件，它能给出与其感应面垂直磁场分量成正比的直流电压输出。当恒定电流流过探头时，载流子受到磁力作用，导致一侧电荷积累，产生霍尔电压 VH。该电压与 B 成正比。霍尔探头在出厂时已经校准，但也可以用已知磁场进行检验。在实验室中，霍尔探头用于描绘磁铁两极之间的磁场分布，研究磁场的均匀性，并在特定点测量 B。对于永磁体，将探头放在磁隙中心并旋转以找到最大读数，该读数对应于垂直磁场分量。
Before taking measurements, the Hall probe must be zeroed. Place the probe in a region of zero magnetic field (or shield it with a mu-metal cylinder) and adjust the zero offset. Then carefully position the probe in the field under investigation. Move the probe systematically along a line between the poles and record the voltage at regular intervals. Convert voltage to magnetic flux density using the calibration factor. A typical error source is the probe’s orientation: if it is not exactly perpendicular to the field, the reading will be lower. Also, the probe’s sensitive area is not a point, so it gives an average reading over its surface area, which can affect spatial resolution. Temperature fluctuations can also affect the semiconductor, so allow the equipment to warm up.
在测量之前，霍尔探头必须调零。将探头置于零磁场区域（或用高导磁合金圆筒屏蔽），调节零偏移。然后小心地将探头放入待测磁场中。沿着磁极之间的直线系统移动探头，并每隔一定间隔记录电压。利用校准系数将电压转换为磁通密度。一个常见的误差来源是探头的方向：如果它没有完全垂直于磁场，读数就会偏低。此外，探头的敏感区域不是一个点，因此它给出的是其表面积上的平均值，这会影响空间分辨率。温度波动也会影响半导体性能，因此需要让设备预热。
3. Investigating the Force on a Charged Particle: e/m Measurement | 探究带电粒子受力：电子比荷测定
duce a uniform magnetic field. Electrons are accelerated through a known potential difference V and enter a region where a magnetic field B is perpendicular to their velocity. The magnetic force acts as a centripetal force: Bev = mv²/r, where v is the electron speed, m its mass, and r the radius of the circular path. Combining with the kinetic-energy relation ½mv² = eV gives e/m = 2V/(B²r²). By measuring the accelerating voltage V, the magnetic field B (calculated from the coil current and geometry), and the radius r of the electron beam, students can compute e/m and compare it to the accepted value of 1.76 × 10¹¹ C kg⁻¹.
测量电子比荷 (e/m) 的经典实验使用细束管或偏转管与亥姆霍兹线圈产生匀强磁场。电子经过已知电势差 V 加速后进入垂直其速度的磁场 B 中。磁力充当向心力：Bev = mv²/r，其中 v 为电子速度，m 为其质量，r 为圆形轨道半径。结合动能关系 ½mv² = eV 可得 e/m = 2V/(B²r²)。通过测量加速电压 V、磁场 B（由线圈电流和几何参数计算）以及电子束的半径 r，学生可以计算出 e/m 并与公认值 1.76 × 10¹¹ C kg⁻¹ 进行比较。
re the room is darkened. Increase the heater current to produce a visible electron beam, then apply the accelerating voltage. Adjust the Helmholtz coil current until the beam curves into a complete circle. Measure the orbit diameter carefully with a ruler or, better, by observing the beam against a mirrored scale to avoid parallax error. Record V, the coil current I, and the radius r. The magnetic field B at the centre of Helmholtz coils of radius R and N turns is B = (8μ₀NI)/(5√5 R). Compute e/m. Repeat for different voltages and coil currents. Key sources of error include the measurement of the beam diameter (the beam has finite thickness), the precision of the voltage and current meters, and the uniformity of the magnetic field. Also, the Earth’s magnetic field may contribute a small systematic error.
实验步骤：将细束管连接到高压电源，亥姆霍兹线圈连接到低压直流电源。在通电前确保房间变暗。增加灯丝电流以产生可见电子束，然后施加加速电压。调节亥姆霍兹线圈电流直到电子束弯曲成完整的圆形。用尺子仔细测量轨道直径，更佳的方法是观察光束在镜面标尺上的位置以避免视差误差。记录 V、线圈电流 I 和半径 r。亥姆霍兹线圈半径为 R、匝数为 N 时，中心磁场 B = (8μ₀NI)/(5√5 R)。计算 e/m。对不同电压和线圈电流重复测量。主要的误差来源包括光束直径的测量（光束具有有限厚度）、电压和电流表的精度，以及磁场的均匀性。此外，地磁场也可能引入一个小的系统误差。
4. Faraday’s Law of Electromagnetic Induction | 法拉第电磁感应定律
Faraday’s law states that the magnitude of the induced e.m.f. in a circuit is equal to the rate of change of magnetic flux linkage through the circuit. This can be investigated by dropping a bar magnet through a coil, moving a magnet in and out of a coil, or rotating a coil in a magnetic field. The most common school experiment uses a coil connected to a datalogger or an oscilloscope, and a strong bar magnet. When the magnet is dropped through the coil, the changing flux induces an e.m.f. pulse. The area under the voltage–time graph is proportional to the total flux change, which should be equal for entry and exit if the magnet’s speed at entry and exit were the same. However, the magnet accelerates due to gravity, so the exit pulse is taller and narrower.
法拉第定律指出，回路中感应电动势的大小等于穿过回路的磁通量链的变化率。可以通过让条形磁铁穿过线圈、将磁铁移入和移出线圈或在磁场中转动线圈来研究这一定律。最常见的学校实验使用连接到数据记录器或示波器的线圈和一块强条形磁铁。当磁铁穿过线圈下落时，变化的磁通量会感应出一个电动势脉冲。电压-时间曲线下的面积与总磁通变化量成正比，如果磁铁进入和离开时的速度相同，则两者面积应相等。然而，由于重力作用，磁铁会加速，因此离开脉冲更高更窄。
the coil. Use a photogate or a motion sensor to measure the speed of the magnet as it enters and exits the coil. Alternatively, use a motor to rotate a coil at a constant angular frequency in a uniform magnetic field and record the a.c. voltage induced. This directly demonstrates that the peak e.m.f. is proportional to the angular speed (ε = NBAω). For the dropping magnet experiment, analyse the area under the peaks by integration. Verify that the total charge flowing (induced e.m.f. / resistance) is related to the total flux change. Errors include the bouncing of the magnet inside the coil, the alignment of the magnet’s motion along the coil axis, and the stray field of the magnet affecting the readings.
要进行定量研究，需要更可控的设置。将线圈垂直安装，从线圈上方已知高度释放磁铁。使用光电门或运动传感器测量磁铁进入和离开线圈时的速度。或者，使用电机让线圈在匀强磁场中以恒定角速度旋转，并记录产生的交流电压。这直接证明峰值电动势与角速度成正比 (ε = NBAω)。对于磁铁下落实验，通过对峰的积分分析面积。验证流过的总电荷（感应电动势/电阻）与总磁通变化量有关。误差包括磁铁在线圈内的弹跳、磁铁运动与线圈轴线的对齐以及磁铁的杂散场对读数的影响。
5. Lenz’s Law and Magnetic Braking | 楞次定律与磁制动
Lenz’s law states that the direction of an induced current is such that it opposes the change in magnetic flux that produced it. A dramatic demonstration involves dropping a strong neodymium magnet down a copper or aluminium tube. The magnet takes several seconds to fall through, much longer than a non-magnetic object of the same mass. As the magnet falls, the changing flux induces eddy currents in the conducting tube. These currents generate their own magnetic field which, by Lenz’s law, opposes the motion of the magnet, producing a retarding force. This is an example of magnetic braking. The experiment can be analysed by timing the fall and comparing it to free fall.
楞次定律指出，感应电流的方向总是使其阻碍产生它的磁通量变化。一个生动的演示是让一块强力钕磁铁穿过一根铜管或铝管落下。磁铁需要好几秒才能穿过，比相同质量的非磁性物体慢得多。磁铁下落时，变化的磁通量在导电管中感应出涡流。这些涡流产生自己的磁场，根据楞次定律，该磁场阻碍磁铁的运动，从而产生一个制动力。这是磁制动的一个例子。该实验可以通过记录下落时间并与自由落体比较来分析。
Quantitative investigations can use a motion sensor or a high-speed camera to track the magnet’s velocity. For a vertical tube, the magnet quickly reaches a terminal velocity, where the magnetic braking force equals the weight. Measure the terminal velocity for different tube materials and wall thicknesses, as the eddy currents depend on the conductivity and geometry. Students can also vary the strength of the magnet. A simple timing experiment: drop the magnet from just above the tube and measure the time to exit. Predict the time for free fall and note the large discrepancy. Safety: neodymium magnets are very strong and can shatter if they slam together, so handle with care. Keep magnets away from electronic devices.
定量研究可以使用运动传感器或高速摄像机跟踪磁铁的速度。对于垂直管，磁铁会很快达到终端速度，此时磁制动力等于重量。测量不同管材和壁厚下的终端速度，因为涡流取决于导体的电导率和几何形状。学生也可以改变磁铁的强度。一个简单的计时实验：让磁铁从管口上方释放并测量离开的时间。预测自由落体的时间，并观察巨大差异。安全方面：钕磁铁磁性极强，猛烈撞击会碎裂，因此要小心操作。让磁铁远离电子设备。
6. Investigating the Transformer | 变压器探究
ore, which links the secondary coil and induces an alternating e.m.f. The ideal transformer equation is Vₛ/Vₚ = Nₛ/Nₚ, where Vₛ and Vₚ are the secondary and primary voltages and Nₛ and Nₚ the numbers of turns. In practice, there are energy losses due to resistive heating, eddy currents, and hysteresis in the core. The efficiency is defined as (output power / input power) × 100% emountable transformer kit with coils of different turn numbers and a laminated iron core.
变压器由绕在公共铁芯上的两个线圈组成。初级线圈中的交流电在铁芯中产生变化的磁通量，该磁通量链接着次级线圈并感应出交流电动势。理想变压器方程为 Vₛ/Vₚ = Nₛ/Nₚ，其中 Vₛ 和 Vₚ 为次级和初级电压，Nₛ 和 Nₚ 为匝数。实际上，由于电阻发热、涡流和磁滞效应，存在能量损耗。效率定义为（输出功率/输入功率）× 100%。学生可以使用可拆卸变压器套件，搭配不同匝数的线圈和叠片铁芯来研究这些原理。
Set up the primary coil with a known number of turns (e.g., 200) connected to an a.c. supply (signal generator or low-voltage a.c.). Connect the secondary coil (e.g., 100 turns) to a voltmeter. Measure the input and output voltages for different turn ratios. Plot Vₛ against Vₚ to check linearity. For efficiency, connect a load resistor across the secondary and measure the currents using a.c. ammeters. Calculate input power (VₚIₚ) and output power (VₛIₛ). Observe that the efficiency improves with a laminated core compared to a solid iron bar, as laminations reduce eddy currents. Also investigate the effect of frequency on output voltage: at low frequencies the core may saturate. Key errors include the voltage drops in the coils (you are measuring terminal voltages, not induced e.m.f.s) and power losses in the meters. Use a cathode ray oscilloscope (CRO) to observe waveforms and see if there is any distortion.
用已知匝数的初级线圈（如 200 匝）连接交流电源（信号发生器或低压交流电）。将次级线圈（如 100 匝）连接到电压表。测量不同匝数比下的输入和输出电压。以 Vₛ 对 Vₚ 作图以检查线性。对于效率，在次级侧连接一个负载电阻，用交流电流表测量电流。计算输入功率 (VₚIₚ) 和输出功率 (VₛIₛ)。观察到与实心铁棒相比，叠片铁芯的效率更高，因为叠片减少了涡流。还可以研究频率对输出电压的影响：低频时铁芯可能饱和。主要误差包括线圈中的电压降（你测量的是端电压，而非感应电动势）以及仪表中的功率损失。使用阴极射线示波器 (CRO) 观察波形，查看是否有畸变。
7. Investigating Magnetic Flux Linkage with a Search Coil | 用探测线圈研究磁通量链
r flipped through 180°), the change in flux linkage induces an e.m.f. pulse that can be integrated by a ballistic galvanometer or an electronic integrator. The total charge displaced is proportional to the change in flux linkage Δ(NΦ) = R × charge, where R is the total circuit resistance. This method can be used to map the field of a magnet, measure the flux density inside a solenoid, or investigate the Earth’s magnetic field. For a solenoid, the flux density inside is given by B = μ₀nI, where n is the number of turns per unit length. By placing the search coil at the centre and flipping it, you can verify this formula.
探测线圈是一个小型线圈，用于测量空间中某点的磁通量或磁通密度。当线圈快速从磁场中移出（或翻转 180°）时，磁通量链的变化会感应出一个电动势脉冲，该脉冲可以用冲击电流计或电子积分器进行积分。移动的总电荷与磁通量链的变化 Δ(NΦ) 成正比，Δ(NΦ) = R × 电荷，其中 R 为回路总电阻。此方法可用于绘制磁铁的磁场、测量螺线管内的磁通密度或研究地磁场。对于螺线管，内部磁通密度由 B = μ₀nI 给出，其中 n 为单位长度匝数。通过将探测线圈置于中心并翻转，可以验证这个公式。
Calibrate the system using a known flux change, e.g., by using a standard solenoid with a known B, or by using a mutual inductance arrangement. Connect the search coil in series with a ballistic galvanometer. Set up a long solenoid carrying a known d.c. Place the search coil at the midpoint, aligned with the axis. Quickly withdraw the coil to a region of zero field and note the galvanometer throw. The throw is proportional to the flux linkage through the search coil. Repeat several times to average. Then change the solenoid current and verify that the throw is proportional to I. To measure the Earth’s horizontal component, orient a large coil with many turns in the Earth’s field and flip it, recording the charge. Common mistakes: not flipping quickly enough (the galvo integrates by impulse), having the search coil too large so that it averages a non-uniform field, and contact resistance in the circuit affecting R.
使用已知的磁通变化来校准系统，例如通过已知 B 的标准螺线管或通过互感装置。将探测线圈与冲击电流计串联。设置一个通有已知直流电的长螺线管。将探测线圈放置在中心点，与轴线对齐。快速将线圈抽出至零场区域并记录电流计的偏转。偏转与通过探测线圈的磁通量链成正比。重复几次取平均。然后改变螺线管电流，验证偏转是否与 I 成正比。要测量地磁水平分量，将一个匝数很多的大线圈在地磁场中定向并翻转，记录电荷。常见错误：翻转速度不够快（电流计通过冲量积分），探测线圈太大导致对非均匀场取平均，以及电路中的接触电阻影响 R。
8. The Magnetic Force on a Moving Charge: Cathode Ray Tube Deflection | 运动电荷的磁力：阴极射线管偏转
be, the beam deflects perpendicularly to both the field and the beam direction, as predicted by Fleming’s left-hand rule. For quantitative work, a pair of Helmholtz coils is placed outside the tube to produce a uniform field over the deflection region. The deflection y on the screen is measured for different coil currents. The electron speed v is determined from the accelerating voltage V (eV = ½mv²). The magnetic force causes a circular arc inside the tube, resulting in an angular deflection. The geometry of the tube yields a relationship that can be used to verify the force equation.
阴极射线管 (CRT) 可用于演示磁场中电子束的受力。当条形磁铁靠近管子侧面时，束流会垂直于磁场和束流方向偏转，这符合弗莱明左手定则。定量研究时，将一对亥姆霍兹线圈放置在管外，在偏转区域产生均匀磁场。测量不同线圈电流下屏幕上的偏转 y。电子速度 v 由加速电压 V 决定 (eV = ½mv²)。磁力使管内产生一段圆弧，导致角度偏转。管子的几何关系可用来验证力的公式。
t deflection y on the calibrated screen. The magnetic field B is known from the coil current. The radius of curvature r of the beam can be deduced from the deflection geometry: if the beam travels a length L inside the field and then a distance D to the screen, a small angle approximation gives r ≈ L²/(2y) if D>>L, or a more precise formula can be used. Compute the magnetic force required and compare with Bev. Alternatively, use a fine-beam tube that shows the complete circular path, as described earlier. Errors include the distortion of the field by the CRT’s internal shielding, the non-uniformity of the screen’s phosphor response, and measurement of small deflections.
将 CRT 与其内部电源一起设置好。将亥姆霍兹线圈垂直于管轴放置。通入已知线圈电流，记录校准屏幕上光点的偏转 y。磁场 B 由线圈电流可知。束流的曲率半径 r 可以从偏转几何中推导出来：如果束流在磁场中行进长度 L 然后到屏幕距离 D，小角度近似下若 D>>L 则 r ≈ L²/(2y)，或者使用更精确的公式。计算所需的磁力并与 Bev 比较。另一种方法是使用细束管显示完整的圆形路径，如前所述。误差包括 CRT 内部屏蔽层对磁场的扭曲、屏幕磷光体响应的不均匀性以及小偏转的测量。
9. Investigating the Magnetic Field of a Solenoid | 探究螺线管磁场
e can map the flux density along the axis of a solenoid and across its diameter. For an ideal infinite solenoid, B = μ₀nI. For a finite solenoid, the field at the centre is slightly less, and at the ends it is approximately half the central value. Students can investigate this relationship by varying the current I and the turn density n (by using solenoids of different lengths or by tapping at different numbers of turns per unit length).
长直螺线管内部的磁场是均匀且平行于轴线的；靠近两端处磁场减弱并扩散开来。使用霍尔探头可以描绘沿螺线管轴线和沿其直径方向的磁通密度分布。对于理想的无限长螺线管，B = μ₀nI。对于有限长螺线管，中心处的磁场略小，而两端处约为中心值的一半。学生可以通过改变电流 I 和匝数密度 n（使用不同长度的螺线管或抽头以改变单位长度匝数）来研究这一关系。
ove the probe in small steps from one end to the other, recording the Hall voltage and hence B. Plot B against axial distance. The plot should be flat in the middle and drop near the ends. Compare the central B with the theoretical value B = μ₀nI. The effective n must be carefully measured: count the number of turns over a measured length. With a long solenoid, the end effects are smaller. To investigate the effect of n, use different solenoids with varying turns per metre, or move the Hall probe along the radius to show that the field is uniform across the cross-section. Common sources of error: the solenoid’s axis must be aligned with the probe’s sensitive direction, the probe’s zero drift, and the Earth’s field may contribute a background reading. Subtract the background by taking a reading with zero solenoid current.
搭建一个大型空心螺线管，连接到直流电源和电流表。将霍尔探头沿轴线放在米尺上。探头调零。从一端到另一端以微小步长移动探头，记录霍尔电压并由此得到 B。绘制 B 随轴向距离的变化图。图中部应平坦，两端附近下降。将中心 B 与理论值 B = μ₀nI 比较。有效 n 必须仔细测量：计算一定长度内的匝数。对于长螺线管，端部效应较小。要研究 n 的影响，可使用每米匝数不同的多个螺线管，或沿半径方向移动霍尔探头以显示横截面内磁场是均匀的。常见误差来源：螺线管轴线必须与探头灵敏方向对齐，探头的零点漂移，以及地磁场可能对背景读数有贡献。通过读取零螺线管电流时的读数来扣除背景。
10. Magnetic Hysteresis in Ferromagnetic Materials | 铁磁材料的磁滞回线
Ferromagnetic materials such as iron display hysteresis when placed in a varying magnetic field. The magnetic flux density B in the material is not a single-valued function of the applied magnetic field strength H, but depends on the previous history of magnetisation. A hysteresis loop can be traced using a CRO and a circuit with a primary coil (creating H) and a secondary coil (sensing B). The primary current produces H, which is proportional to the voltage across a series resistor, and the secondary voltage is integrated to give B. The area of the hysteresis loop represents the energy loss per cycle per unit volume of the material, important for transformer core design.
铁磁材料（如铁）在变化的磁场中会表现出磁滞现象。材料中的磁通密度 B 并不是外加磁场强度 H 的单值函数，而是依赖于之前的磁化历史。可以使用 CRO 和包含初级线圈（产生 H）和次级线圈（检测 B）的电路来描绘磁滞回线。初级电流产生 H，它与串联电阻两端的电压成正比；次级电压经过积分得到 B。磁滞回线的面积代表材料每周期单位体积的能量损耗，这对变压器铁芯设计很重要。
Construct a circuit: a primary coil wound on a toroidal iron core, driven by an a.c. source (variable frequency). The current through the primary is monitored by the voltage across a small resistor, giving a signal proportional to H. A secondary coil is also wound on the core and connected to an integrating circuit (a large capacitor in parallel with a resistor). The voltage across the capacitor is proportional to B. Feed the H signal to the x-input of the CRO and the B signal to the y-input. Adjust the amplitude and observe the hysteresis loop. Increase the primary current until the loop tips flatten – saturation. Measure the loop area by tracing on graph paper or using the oscilloscope’s measure functions. The coercive force and remanence can be determined from the intercepts. Variations: compare different core materials (soft iron, ferrite, steel). Soft iron gives a narrow loop with low energy loss, while steel gives a broad loop. Errors include integrator drift, stray fields, and non-uniform winding.
构建电路：在环形铁芯上绕制初级线圈，由交流源（可变频率）驱动。通过初级线圈的电流用一个小电阻两端的电压监测，该信号与 H 成正比。在铁芯上也绕制一个次级线圈并连接到积分电路（一个大电容与电阻并联）。电容两端的电压与 B 成正比。将 H 信号送到 CRO 的 x 输入，B 信号送到 y 输入。调整幅度并观察磁滞回线。增大初级电流直到回线顶端变平——饱和。通过用坐标纸描图或使用示波器的测量功能来测量回线面积。矫顽力和剩磁可从截距求得。变型实验：比较不同铁芯材料（软铁、铁氧体、钢）。软铁产生窄回线，能量损耗低；钢产生宽回线。误差包括积分器漂移、杂散场和绕组不均匀。
11. Eddy Current and Magnetic Damping Experiments | 涡流与磁阻尼实验
Eddy currents are circulating currents induced in a conductor when it experiences a changing magnetic field. These can be demonstrated and quantified by allowing a magnet to swing as a pendulum over a copper or aluminium sheet, or by dropping a sheet of metal between the poles of a magnet. In the pendulum setup, a metal plate attached to a rigid pendulum is allowed to swing freely into the gap of a strong magnet. When the plate enters the field, eddy currents produce a damping force that quickly reduces the amplitude. Without the magnet, the pendulum swings for a long time. This is a clear demonstration of electromagnetic damping, used in electromagnetic brakes and induction stove tops.
涡流是导体在变化磁场中时感应出的循环电流。可以通过让磁铁在铜板或铝板上方作单摆运动，或让金属板在磁极之间下落来演示和量化涡流。在单摆装置中，将金属板连接到一个刚性摆上，让其自由荡入强磁铁的间隙。当金属板进入磁场时，涡流产生一个阻尼力，迅速减小振幅。没有磁铁时，摆会持续摆动很长时间。这清晰地演示了电磁阻尼，应用于电磁制动器和电磁炉。
Quantitative experiment: use a light-gate to measure the velocity of the pendulum as it enters and leaves the field. The loss in kinetic energy equals the work done by the eddy current drag force. Alternatively, fix a metal strip on a low-friction linear air track, and place a row of magnets along the track. As the slider passes over the magnets, it decelerates. Measure the deceleration and relate it to the velocity – the drag force is often proportional to the velocity. Another variation: suspend a magnet from a spring and let it oscillate above an aluminium plate. The damping constant can be found from the logarithmic decrement of the amplitude. The experiments reveal that the eddy current force depends on the conductivity and thickness of the metal, as well as the relative velocity. Good for evaluating Lenz’s law and energy conservation, as the induced currents dissipate heat in the metal.
定量实验：使用光门测量摆进入和离开磁场时的速度。动能的损失等于涡流阻力做的功。另一种方法是将金属条固定在一个低摩擦线性气垫导轨上，沿导轨放置一排磁铁。当滑块经过磁铁上方时会减速。测量减速度并将其与速度关联——阻力往往与速度成正比。又一个变型：将磁铁悬挂在弹簧上，让其在铝板上方振荡。通过振幅的对数衰减可以求出阻尼常数。这些实验揭示涡流力取决于金属的电导率和厚度以及相对速度。适合评估楞次定律和能量守恒，因为感应电流会在金属中耗散热量。
12. Safety and Precision in Magnetic Field Experiments | 磁场实验中的安全与精度
Magnetic field experiments often involve high currents, strong magnets, and delicate equipment. High currents can cause burns from hot wires or components; always use insulated wires and check ratings. Strong permanent magnets, especially neodymium magnets, can cause serious injury if they snap onto a metal surface or each other, trapping skin. Keep them separated and handle with gloves and eye protection. Cathode ray tubes and fine-beam tubes use high voltages (EHT) – always have a competent supervisor and ensure all connections are secure before switching on. Wait for capacitors to discharge before handling circuits. Also, large electromagnetic fields can affect pacemakers, so be aware of anyone with medical implants.
磁场实验通常涉及大电流、强磁铁和精密设备。大电流可能导致导线或元件发热烫伤；务必使用绝缘导线并检查额定值。强力永磁体，特别是钕磁铁，如果猛然吸附到金属表面或彼此吸合，会造成严重伤害，夹伤皮肤。要将它们分开并佩戴手套和护目镜操作。阴极射线管和细束管使用高电压（EHT）——必须由有资质的主管指导，并确保所有连接牢固后才通电。在处理电路前等待电容器放电。此外，强电磁场可能影响心脏起搏器，因此要注意有医疗植入物的人员。
Precision in measurement requires careful zeroing of probes and meters, avoidance of parallax in reading scales, and minimisation of systematic errors. For Hall probes, ensure temperature stabilisation and correct orientation. For current
Published by TutorHao | A-Level Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图