自感 - 定义、系数、影响因素、应用

当由铜线制成的线圈置于磁场中时，磁通量会被添加到线圈中。法拉第发现，当附着在线圈上的磁通量被充电时，电流会被引入线圈，前提是线圈是闭合的。如果线圈开路，则线圈中会产生电动势。因此产生的电流和电动势分别称为感应电流和感应电动势。只要与线圈相关的磁通量发生变化，线圈中的感应电流和电动势就会移动。

电感

导体或电路的特性，由于电流的变化而产生电动势。密绕线圈的磁通量与连接电流成正比，即∅ _B ∝ I。

对于 N 匝闭合绕组线圈，相同的磁通量连接在所有绕组上。随着通过线圈的磁通量 ∅ _B发生变化，每一匝都会产生感应电动势。因此，与线圈相连的磁通（磁链）等于 N×∅ _B。

然后，总通量，N∅ _B ∝ I。

上述反应中的比例常数 (I) 称为电感。

自感应

The phenomenon according to which an inversely induced electromotive force occurs as a result of a change in electric current or magnetic flux in a coil is called self-induction. or we can define it as the phenomenon of production of induced emf in a coil changes when an electric current is passed through it. 

Can also be expressed in words because the potency of the current in the coil, current in the coil also changes. In such a situation an emf is induced in the coil as well. Such emf is called self-induced emf and this phenomenon is known as self-induction.

自感是线圈的特性，因此，线圈通过自身感应电动势来抵抗流过它的电流强度的任何变化。

感应电动势也称为反电动势。当线圈中的电流打开时，自感应反对电流的增加，而当电流关闭时，自感应反对电流的损失。自感应是众所周知的电的惯性。

线圈的自感 L 取决于-

1. 线圈的大小和形状。
2. 匝数N。
3. 存在磁通的线圈内介质的磁性。

Note: Self-induction L does not depend on the current I.

自感系数公式：与线圈相连的总磁通量， N∅ ∝ I

N∅ = L

其中∅ = 与每匝相关的磁通，L = 自感的自感系数。

此外，感应电动势，

e= -(d∅/ d × t) = -L dI/dt

在哪里

L = ε/(dl / d × t)

1 亨利 (H) = 1V – s / A 或 1 T × m ² / A或ohm-s。

自感

长螺线管的自感

A long solenoid is one whose length is much larger than the radius of the cross-section.

Derivation for self-inductance of Long Solenoid formula-

The magnetic field (B) at any point inside alike a solenoid is realistically constant and is specified by-

B = µ°NI/L                                                                                                                                                                                              ……(1)

where,

• μ_°= absolute magnetic permeability of free space, 
• N= total number of turns in the solenoid 
• l =length of the solenoid. 

Magnetic flux using every inflexion of the solenoid, 

∅=B × area of each turn

∅ = µ_°NI/L × A

where A  area of all inflexion of the solenoid.

Total magnetic flux fascinated the solenoid = flux through every turn × total number of turns

N∅ = µ_°I × (N/L) × AI × N

If L is the coefficient of self-inductance of the solenoid, then 

N*∅ = LI                                                                                                                                                                                                       …….(2)

From Equations 1 and 2, we get

L = (µ_°I N² A) / l

It gives the self-Inductance of al long solenoid of length l, area of cross-section. A is having a number of turns per unit length equal to N. If the core is of any other magnetic material u is placed, then 

μ= μ_° μ_r

L = (µ_° µ_r N² A) / l

The magnitude of emf is given by

e = L(dI × dt)

Multiplying (I) to both sides, we get 

el × dt = LI × dl                                                                                                                                                                                             …….(3)

But

I × dt = dq

Also, work done (dW) = voltage (e) x charge (dq) or dW=e x dq=el × dt

deputize these values in equation 3, we get

dW = LI × dl     .                                                                                                                                                                                           …….(4)

Total work done in increasing the current from zero to I_° we have By integrating both sides of equation 4 we get

W = ½ × LI_° ²

This work done in increasing the current flowing through the inductor is stored as the potential energy (U) in the magnetic field of the inductor.

U =  ½ × LI_° 2

影响螺线管周围磁场强度的因素

• 匝数（扭转） 匝数越大，螺线管的磁场越强，反之亦然。
• 流动的电流量。
• 通量越大，磁场越强，反之亦然。
• 沿螺线管轴线放置软铁芯可增加磁场强度。

自感的应用

自感的一些应用是：

• 变形金刚
• 调谐电路
• 感应电机
• 传感器
• 在设备中储存能量
• 铁氧体磁珠
• 扼流圈
• 过滤器
• 用作继电器的电感器

示例问题

问题一：什么是电的惯性？

回答：

When a source of emf sends current in a coiled electric circuit, the self-inductance of the inductor (coil) behaves in the same way as the mass of a body, when a force causes a change in its position. , We know that the greater the mass of a body, the more it opposes the change in the state of the body. Similarly, the mass of a body gives a measure of its inertia. Similarly, the greater the self-inductance of a coil, the greater is its resistance to the change in current through the coil. That’s why self-inductance is also known as the inertia of electricity.

问题2：解释为什么感应线圈是用铜制成的。

回答：

The ohmic resistance of an induction coil made of copper will be very low. Due to the change in magnetic flux, a large induced current will be generated in such an inductance, offering considerable opposition to the flow of current due to the applied emf.

问题 3：哪些因素控制着电路中电动势的大小？

回答：

The magnitude of the induced emf in an electric circuit is proportional to the rate of change of the magnetic flux associated with the circuit.

问题4：让两个大小相同的圆球，一个是金属的，一个是玻璃的，从离地相同高度自由落下。两者中哪一个会先到达，为什么？

回答：

The glass bob will reach earlier on the ground as acceleration due to gravity is independent of the mass of the falling bodies. Being an insulator, no induced current is developed in it due to the earth’s magnetic field.

问题 5：给定线圈的自感如何增加 N 匝数、面积和横截面 A 的长度/？

回答：

The self-inductance can be increased with the help of electric fields. It does not depend on the current through the circuit but depends upon the permeability of the material from which the core is made up off.