The Magnetic Field • •

A permanent magnet has a magnetic field surrounding it. A magnetic field is envisioned to consist of lines of force that radiate from the north pole to the south pole and back to the north pole through the magnetic material.

Attraction and Repulsion • •

Unlike magnetic poles have an attractive force between them. Two like poles repel each other.

Altering a Magnetic Field • •

When nonmagnetic materials such as paper, glass, wood or plastic are placed in a magnetic field, the lines of force are unaltered. When a magnetic material such as iron is placed in a magnetic field, the lines of force tend to be altered to pass through the magnetic material.

Magnetic Flux •

•

The force lines going from the north pole to the south pole of a magnet are called the magnetic flux (φ). The number of lines of force in a magnetic field determines the value of the flux – the more lines of force, the greater the flux and the stronger the magnetic field. The unit of magnetic flux is the weber (Wb), and one Weber = 108 lines. The magnetic flux density (B) is the amount of flux per unit area perpendicular to the magnetic field. In other words, the more lines of force, the greater the flux and therefore the greater the flux density. Magnetic flux density is a measure of how many lines of force flow through a given area. The unit of magnetic flux density is the tesla (T)1. B=

φ A

Magnetizing Materials Ferromagnetic materials such as iron, nickel and cobalt have randomly oriented magnetic domains, which become aligned when placed in a magnetic field, thus they effectively become magnets.

1

Although the SI unit for flux density is the Tesla, another unit called the gauss is sometimes used. The measurement of flux density is accomplished using a meter called a gaussmeter. A degaussing function is included with most monitors in order to prevent the buildup of magnetic fields.

Electromagnetism • • •

Electromagnetism is the production of a magnetic field by current in a conductor. Whenever current flows through a conductor, magnetic lines of force are produced in concentric circles around the conductor. These lines of force are collectively referred to as an electromagnetic field Electromagnets are used in devices such as tape recorders, electric motors, speakers, solenoids, and relays.

Direction of Lines of Force • The direction of the lines of force surrounding a conductor depend upon the direction of current flow. • The right-hand rule is used to determine the direction of the lines of force. • If the conductor is grasped in the right hand, with the thumb pointing in the direction of current flow, the fingers of the right hand point in the direction of the magnetic lines of force.

Permeability • • • •

Permeability (µ) is the ease with which a magnetic field can be established in a given material. The higher the permeability, the more easily a magnetic field can be established. Relative permeability (µr) of a material is the ratio of its absolute permeability to the permeability of a vacuum. Materials with high permeability’s are collectively referred to as ferromagnetic materials. These include iron, steel, nickel, cobalt and alloys formed from these materials. µr =

µ µ0

where µ 0 = 4πx10−7 Wb / At.m

Reluctance • • •

The opposition to the establishment of a magnetic field in a material is called reluctance (ℜ). Reluctance is analogous to resistance in an electric circuit. Materials with high permeability’s have low reluctance and vice versa. ℜ=

1 in At/Wb µA

Magnetomotive Force • • •

The force that produces the magnetic flux lines in a material is called the magnetomotive force ( Fm ) The magnetomotive force (Fm) depends upon the number of turns of wire, and the amount of current through the wire. The unit of mmf is the ampere=turn (At) which is established on the basis of the current in a single loop (turn) of wire. The mmf is defined as the amount of current flowing in one turn of wire multiplied by the total number of turns of wire: Fm = NI

Ohm’s Law for Magnetic Circuits Magnetomotive force, Reluctance and flux in magnetic circuits are related in a manner analogous to voltage, resistance and current in electronic circuits: Φ=

Fm ℜ

OR

Fm = Φℜ

The preceding equation is therefore often referred to as ohm’s law for magnetic circuits.

Example: How much flux is established in the magnetic path in the following figure if the reluctance of the material is 28 x103 At / Wb ?

Answer: 536 µWb

The Electromagnet • •

An electromagnet is a coil of wire wound around a core material that can be easily magnetized. The poles of the magnet depend upon the direction of current flow.

Example: A crankshaft position sensor that produces a voltage when a tab passes through the air gap of the magnet.

As the tab passes through the air gap of the magnet, the coil senses a change in the magnetic field, and a voltage is induced.

Magnetizing Force Whereas the magnetomotive force describes the force that produces a magnetic field, the magnetizing force (H) is a measure of how much magnetomotive force exists per unit length (l) of a material: H =

Fm in At/m l

Note that both the flux density (B) and the magnetizing force (H) increase as the magnetomotive force (Fm) increases

Magnetizing a Material • •

When a magnetic material is exposed to a magnetizing force, it will remain magnetized even with the magnetizing force removed; this is termed retentivity. Reversal of the magnetizing force will cause the flux density to move toward its negative maximum value.

The B-H curve shown in (g) above is known as the Hysteresis curve

Retentivity - A measure of the residual flux density corresponding to the saturation induction of a magnetic material. In other words, it is a material's ability to retain a certain amount of residual magnetic field when the magnetizing force is removed after achieving saturation. Residual Magnetism or Residual Flux - the magnetic flux density that remains in a material when the magnetizing force is zero. Note that residual magnetism and retentivity are the same when the material has been magnetized to the saturation point. However, the level of residual magnetism may be lower than the retentivity value when the magnetizing force did not reach the saturation level.

Material Retentivity • • • •

Materials with low retentivity do not retain a magnetic field very well. Permanent magnets and magnetic tape require high retentivity. A tape recorder read/write head requires low retentivity. Low retentivity is desirable in electric motors, since the residual field must be overcome each time the current reverses, thus wasting energy.

Electromagnetic Induction When a conductor is moved through a magnetic field, a voltage is induced across the conductor. This principle is known as electromagnetic induction.

Relative Motion • • • •

When a wire is moved across a magnetic field, there is a relative motion between the wire and the magnetic field. When a magnetic field is moved past a stationary wire, there is also relative motion. In either case, the relative motion results in an induced voltage in the wire. The induced voltage depends on the rate of relative motion between the wire and the magnetic field.

Polarity of Induced Voltage The direction of movement of a wire through a magnetic field will affect the polarity of the induced voltage as indicated below:

Induced Current • • •

The voltage induced by the relative motion of a wire through a magnetic field will cause a current in a load connected to the wire. This current is called an induced current. The concept of induced current is the basis for electric generators.

Motor Action When a current flows through a wire that is in a magnetic field, the direction of current flow will result in the magnetic field being weakened on one side, and strengthened on the other.

• •

The result of the weakened and strengthened field is a force on the conductor. This force is the basis for electric motors.

Faraday’s Law The voltage induced across a coil of wire equals the number of turns in the coil times the rate of change of the magnetic flux. v=N

dφ dt

Lenz’s Law Whereas Faraday’s Law defines the magnitude of the voltage induced in a coil placed in a changing magnetic field, lenz’s law defines the polarity (direction) of the induced voltage. When the current through a coil changes, an induced voltage is created as a result of the changing electromagnetic field, and the direction of the induced voltage is such that it always opposes the change in current.

Summary • • • • • • • • •

Unlike magnetic poles attract each other, and like poles repel each other. Materials that can be magnetized are called ferromagnetic. When there is current through a conductor, it produces an electromagnetic field around the conductor. The right-hand rule can be used to establish the direction of the electromagnetic lines of force around a conductor. An electromagnet is basically a coil of wire around a magnetic core. When a conductor moves within a magnetic field, or when a magnetic field moves relative to a conductor, a voltage is induced across the conductor. The faster the relative motion between a conductor and a magnetic field, the greater is the induced voltage. Faraday’s Law predicts the size of the voltage produced in a coil placed in a changing magnetic field Lenz’s Law predicts the polarity of the induced voltage