Mutual Inductance

Coupled Inductors

耦合电感器

When a steady current flows in one coil as in the left illustration, a magnetic field is produced in the other coil. But since that magnetic field is not changing, Faraday's law tells us that there will be no induced voltage in the secondary coil. But if the switch is opened to stop the current as in the middle illustration, there will be a change in magnetic field in the right hand coil and a voltage will be induced. A coil is a reactionary device, not liking any change! The induced voltage will cause a current to flow in the secondary coil which tries to maintain the magnetic field which was there. The fact that the induced field always opposes the change is an example of Lenz' law. Once the current is interrupted and the switch is closed to cause the current to flow again as in the right hand example, an induced current in the opposite direction will oppose that buildup of magnetic field. This persistent generation of voltages which oppose the change in magnetic field is the operating principle of a transformer. The fact that a change in the current of one coil affects the current and voltage in the second coil is quantified in the property called mutual inductance.

当一个恒定电流在其中一个线圈中流动，如左图所示，另一个线圈中会产生一个磁场。但由于这个磁场不发生变化，法拉第定律告诉我们，次级线圈中不会产生感应电压。但如果开关断开以停止电流，如中图所示，右侧线圈中的磁场会发生变化，并会产生电压。线圈是一种反应性装置，不喜欢任何变化！感应电压将导致次级线圈中产生电流，该电流试图维持原有的磁场。感应磁场总是反对变化这一事实是楞次定律的一个例子。一旦电流中断，开关再次闭合以使电流重新流动，如右图所示，次级线圈中将产生相反方向的感应电流以反对磁场的建立。这种持续产生反对磁场变化的电压是变压器工作原理的体现。电流在其中一个线圈中的变化对第二个线圈中的电流和电压的影响，是互感这一性质的量化描述。

Mutual Inductance

互感

When an emf is produced in a coil because of the change in current in a coupled coil , the effect is called mutual inductance. The emf is described by Faraday's law and it's direction is always opposed the change in the magnetic field produced in it by the coupled coil (Lenz's law ). The induced emf in coil 1 is due to self inductance L.

当一个线圈中的感应电动势是由于耦合线圈中电流的变化而产生时，这种效应称为互感。该感应电动势由法拉第定律描述，并且其方向总是与耦合线圈所产生的磁场变化相反（楞次定律）。线圈1中的感应电动势是由于自感L产生的。

The induced emf in coil #2 caused by the change in current I₁ can be expressed as

由电流I₁的变化在 coil #2 中感应出的电动势可以表示为

The mutual inductance M can be defined as the proportionalitiy between the emf generated in coil 2 to the change in current in coil 1 which produced it.

互感量M可以定义为在 coil 2 中产生的感应电动势与在 coil 1 中产生该感应电动势的电流变化之间的比例关系。

transformer

互感最常见的应用是变压器

Mutual Inductance:Transformer

互感：变压器

When more current flows in the secondary of a transformer as it supplies more power, then more current must flow in the primary as well since it is supplying the energy. This coupling between the primary and secondary is most conveniently described in terms of mutual inductance. The mutual inductance appears in the circuit equations for both the primary and secondary circuits of the transformer.

当变压器次级绕组流过的电流增加以供给更多的功率时，初级绕组中也必须有相应的电流流过，因为它在供给能量。初级与次级之间的耦合最方便地通过互感来描述。互感出现在变压器初级和次级电路的电路方程中。