30.8
法拉第定律
法拉第定律指出，感应电动势是单位时间内磁通量的负变化。 磁场的任何变化或线圈区域相对于磁场的方向的变化都会感应出电压（emf）。 磁通量测量通过一定表面积的磁场线的数量。 磁通量是根据磁场矢量和面积矢量的点积的积分来估计的。 负号描述了感应电动势驱动电路周围电流的方向。 然而，这个方向最容易通过称为…
法拉第定律指出，在闭合导体回路中，感应电动势等于通过该回路的磁通量对时间的负导数。感应电动势的方向后来由楞次给出。
如果导电回路由 N 匝完全相同的线圈组成，且通过每一匝的磁通量均相同，则总磁通量为每匝磁通量的 N 倍。因此，总的感应电动势将等于磁通量变化率乘以 N。
考虑一个边长为0.25米的方形线圈，该线圈由紧密缠绕的500匝导线组成。该线圈置于磁场中，且磁场以每秒0.2特斯拉的速率增加。
然后可根据法拉第定律计算线圈中感应电动势的大小。代入相应数值后，即可估算出感应电动势的大小。
需要注意的是，通过改变这些参数中的任意一个或它们的组合，都可以产生电动势。
View the full transcript and gain access to JoVE Core videos
Q1: What does Faraday's law state about induced emf in a conducting loop?
Faraday's law states that the induced emf in a closed conducting loop equals the negative time derivative of magnetic flux through that loop. This means the induced emf is directly proportional to how quickly the magnetic flux changes. The negative sign indicates the direction of the induced emf, which is determined by Lenz's law. Any change in the magnetic field or coil orientation induces a voltage.
Q2: How does the number of coil turns affect the total induced emf?
When a conducting loop consists of N identical turns with the same magnetic flux through each turn, the total magnetic flux is N times the flux through a single turn. Consequently, the total induced emf is N multiplied by the rate of change of magnetic flux. This relationship allows engineers to increase induced emf by adding more tightly wound turns to the coil.
Q3: What parameters can be changed to induce an emf in a coil?
An emf can be induced by changing the magnetic field strength, the orientation of the coil's area relative to the magnetic field, or a combination of both. For example, if a square coil is placed in an increasing magnetic field, the changing flux induces an emf. Similarly, rotating the coil changes the dot product of the magnetic field and area vectors, also inducing an emf.
Q4: How is magnetic flux calculated and what does it represent?
Magnetic flux measures the number of magnetic field lines passing through a given surface area. It is calculated as the integral of the dot product of the magnetic field vector and the area vector. This calculation accounts for both the field strength and the angle between the field and the surface. Understanding magnetic flux is essential for applying Faraday's law to real-world electromagnetic systems.
Q5: What are practical applications of Faraday's law in everyday devices?
Ground fault interrupter (GFI) devices use Faraday's law as a circuit breaker to prevent electrical shocks. Electric guitars employ the principle when a pick coil near a vibrating string detects changes in magnetic flux caused by the string's motion. This changing flux produces an emf that is amplified to create sound. These applications demonstrate how induced electric fields enable modern technology.
Q6: How would you calculate the induced emf in a specific coil using Faraday's law?
To calculate induced emf, substitute the known values into Faraday's law: emf equals negative N times the rate of change of magnetic flux. For a square coil with 500 turns and 0.25-meter sides in a magnetic field increasing at 0.2 tesla per second, multiply 500 by the area (0.0625 m²) and the field change rate to find the magnitude of induced emf.
Q7: Why is the negative sign important in Faraday's law?
The negative sign in Faraday's law describes the direction in which the induced emf drives current around a circuit, reflecting Lenz's law. This sign indicates that the induced current opposes the change in magnetic flux that created it. While the negative sign is mathematically important, the actual direction is most easily determined using Lenz's law as a practical guide.