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# The Basic Law of the Magnetic Circuit of Electric Machines

The general magnetic field is too complex, and in engineering calculations, the magnetic field problem is usually simplified as a magnetic circuit problem. Usually, the following 5 laws are used. Before learning the 5 laws, understand the magnetic circuit’s physical quantities.

Magnetic circuit: The path through which magnetic flux passes.

Excitation winding: A current-carrying coil generates magnetic flux in a magnetic circuit.

Excitation current: The current in the excitation winding.

DC magnetic circuit: The path through which the magnetic flux generated by DC excitation current passes.

For example, the magnetic circuit of a DC motor.

AC magnetic circuit: The path through which the magnetic flux generated by AC excitation current passes.

For example: transformer.

## 1. Ampere’s Loop Law, Total Current Law (Electromagnetism)

Along any closed circuit, the line integral of the magnetic field intensity equals the algebraic sum of the currents surrounded by the closed circuit.

The direction of the magnetic field intensity on an unclosed circuit in the positive current direction follows a right-hand spiral relationship.

This law is mainly used for magnetic circuit calculation of electric motors.

## 2. Law of Electromagnetic Induction (Dynamic Magnetism Generates Electricity)

The direction of the electromotive force is determined using the right-hand rule.

There are two different ways to cause changes in the magnetic flux of the coil:

1) Transformer electromotive force

If the magnetic flux is generated by alternating current, the magnetic flux changes over time and the resulting electromotive force is called the transformer electromotive force. (The coil is relatively stationary with the magnetic field)

2) Motion electromotive force

Suppose the magnetic flux passing through the coil does not change with time, but relative motion exists between the coil and the magnetic field. In that case, it will also cause changes in the magnetic flux of the coil, and the generated electromotive force is called the motion electromotive force.

3) Another form of motion, electromotive force, is represented by:

The direction of the electromotive force is determined using the right-hand rule.

## 3. Electromagnetic force law

The direction of the electromagnetic force is determined according to the left-hand rule.

Electromagnetic torque: In a rotating motor, the electromagnetic force multiplied by the radius of rotation of the conductor is the electromagnetic torque, which is:

## 4. Ohm’s law of the magnetic circuit

No magnetic branch circuit

The iron core is uniform and equal everywhere, taking the average magnetic path.

Law content: The magnetic electromotive force acting on the magnetic circuit equals the magnetic flux within the magnetic circuit multiplied by the magnetic resistance.

## 5. Kirchhoff’s first law of the magnetic circuit

The content of the law: The magnetic flux passing through (or out of) any closed surface is equal to zero.

Branch magnetic circuit with parallel branches:

## 6. Kirchhoff’s Second Law of Magnetic Circuit

Law content: The algebraic sum of the magnetic electromotive force along any closed magnetic circuit equals the algebraic sum of the magnetic voltage drop of each section of the magnetic circuit.

The magnetic circuit shown comprises two parts: ferromagnetic material and air gap. The cross-sectional area of this part of ferromagnetic material is divided into A1 and A2, so the entire magnetic circuit should be divided into three sections.