# Introduction To Electrical Machines

In the study of electrical machines the fundamentals of electromagnetism and single- and three-phase circuits play the most important role. The main aim of this introductory chapter is to introduce the basics, which are the cornerstones of electrical machines.

**ELECTROMAGNETISM**

When an electric current passes through a conductor, a magnetic field immediately builds up due to the motion of electrons. When a magnetic field encompasses a conductor and moves relative to the conductor, the electrons come in motion. This is the converse of the previous phenomenon. Electromagnetism is the study of electromagnetic force (emf) induced in the conductor when it cuts the magnetic flux or is cut by the magnetic flux.

### DIRECTION OF CURRENT IN A CONDUCTOR

Figure 1(a) shows that there is no current through the conductor. Figure 1(b) shows that the conductor carries current away from the observer, that is, in a downward direction, while Figure 1(c) indicates that the conductor carries current towards the observer, that is, in an upward direction.

### DIRECTION OF MAGNETIC FLUX IN A CONDUCTOR

The direction of magnetic flux can be easily found out by using either the right-hand rule or the corkscrew rule.

**Right-hand rule**: If the conductor is graphed by the right hand in such a way that the thumb points in the direction of the current, then the closed fingers give the direction of flux, as shown in Figure 2.**Corkscrew rule**: Imagine a corkscrew is pointed in the direction of a current. The direction of magnetic field is in the direction in which the screw is to be turned to move it in a forward direction. The application of the corkscrew rule is shown in Figure 3.

**Figure 1** Direction of Current in a Conductor

**Figure 2** Right-hand Rule

**Figure 3** Corkscrew Rule

### FLUX DISTRIBUTION OF AN ISOLATED CURRENT-CARRYING CONDUCTOR

The distribution of flux when a conductor carries current downwards, that is, away from the observer, is shown in Figure 4(a). The flux distribution when a conductor carries current upwards, that is, towards the observer, is shown in Figure 4(b).

### FORCE BETWEEN TWO CURRENT-CARRYING CONDUCTORS

Figures 5(a) and 5(b) show the two conductors *A* and B, carrying current in the same and the opposite directions, respectively. The flux distribution when they carry current in the same direction is shown in Figure 5(a). The magnetic fields set up by the two conductors are in opposite directions. Hence, they attract each other. The flux distribution when they carry current in opposite directions is shown in Figure 5(b). The magnetic fields set up by the two conductors are in the same direction. Hence, they repel each other.

### FORCE ON A CONDUCTOR IN A MAGNETIC FIELD

The force experienced by a current-carrying conductor placed in a magnetic field, shown in Figure 6, is expressed as

*F* = *BIL*

where *F* is the force on the conductor (N), *B* is the magnetic flux density (Wb/m^{2}), *I* is the current in the conductor (A) and *L* is the effective length of the conductor to the field (m).

If *F* = 1N, *I* = 1A and *L* = 1 m, *B* = 1 T.

**Figure 4** Isolated Current carrying Conductors

**Figure 5** Two Current-carrying Conductors

**Figure 6** Conductor at an Angle of 90° to a Magnetic Field

**Figure 7** Conductor at an Angle *θ* to a Magnetic Field

If the conductor is placed at an angle *θ* to the field, as shown in Figure 7, the effective length will be *L*sin *θ* and the force on the conductor will be *F* = *BIL* sin *θ*.

The effective length is the length of the conductor lying within the magnetic field.

If *θ* = 0, that is, the conductor is placed parallel to the field, *F* = 0.

The basic principle of an electric motor is that the armature conductor carrying the current is placed in a magnetic field. So, it is also called the motor principle. The direction of rotation of the armature is defined by Fleming’s left-hand rule, as shown in Figure 8.

**Figure 8** Fleming’s Left-hand Rule

Spread the thumb, forefinger and second finger of the left hand so that they are mutually perpendicular to each other. If the forefinger indicates the direction of flux and the second finger indicates the direction of current, the thumb will indicate the direction of rotation of the armature.