Magnetism and electromagnetism

Electricity and magnetism are two sides of the same phenomenon. Every current produces a magnetic field, and a changing magnetic field produces a voltage. These two facts make possible almost every machine an electrician installs: relays and contactors that switch circuits, solenoid valves, motors that turn pumps and fans, generators that supply the grid, transformers that change voltage, clamp meters that measure current without breaking the circuit, and the magnetic trip elements in circuit breakers. This lesson explains magnets and magnetic fields, the field around a current-carrying conductor and a coil, electromagnets and their uses, the force on a conductor in a magnetic field that drives motors, and electromagnetic induction, which drives generators and transformers.

Magnets and magnetic fields

A magnet has two poles, north and south. Like poles repel and unlike poles attract. The space around a magnet where its force acts is its magnetic field, pictured as lines of magnetic flux that leave the north pole and enter the south pole, forming closed loops. The closer the lines, the stronger the field. Iron filings sprinkled around a magnet line up along these flux lines.

Magnetic flux is measured in webers (Wb), and flux density, the flux per unit area, in teslas (T):

where \(B\) is flux density in teslas, \(\Phi\) is flux in webers and \(A\) is area in square metres. The Earth's field is about 0.00005 T (50 µT); a fridge magnet about 0.005 T; the iron core of a transformer or motor operates at about 1 T to 1.7 T; and an MRI scanner at 1.5 T to 3 T or more.

Materials respond to magnetic fields in different ways. Ferromagnetic materials, such as iron, nickel, cobalt and electrical steels, concentrate flux strongly, and are used in cores of motors, transformers and relays. Permanent magnets (ferrite, alnico, and powerful neodymium-iron-boron magnets) keep their magnetism; they are used in permanent magnet motors, generators in wind turbines, speakers and sensors. Most other materials, including copper, aluminum, plastics and air, are essentially non-magnetic.

The field around a current

In 1820, Hans Christian Ørsted noticed that a compass needle moved near a wire carrying current. Every current-carrying conductor is surrounded by circular magnetic field lines. The direction follows the right-hand rule: grip the conductor with your right hand, thumb pointing in the direction of conventional current (positive to negative), and your fingers curl in the direction of the field. The field weakens with distance from the conductor.

This principle is used by clamp meters (Lesson 7): the jaws surround a single conductor and measure its magnetic field to determine the current. Clamping around both conductors of a circuit gives a reading near zero because their fields cancel, a fact used to detect leakage current.

Coils and electromagnets

Winding a conductor into a coil concentrates the magnetic field: the fields of all the turns add together inside the coil, which then behaves like a bar magnet with north and south poles. The strength of the field depends on the magnetomotive force, the current multiplied by the number of turns:

measured in ampere-turns. Placing an iron core inside the coil multiplies the flux hundreds or thousands of times, because iron has a much higher permeability than air. The result is an electromagnet: a magnet that can be switched on and off with current. Unlike permanent magnets, electromagnets can be controlled, which is why they appear in so much electrical equipment.

Uses of electromagnets

• Relays and contactors: an electromagnet pulls an armature that opens or closes contacts, letting a small control current switch a large load current (ELEC-220 and ELEC-330).
• Solenoids: a plunger pulled into a coil operates valves, door locks and brakes.
• Circuit breakers: a magnetic trip coil carrying the circuit current pulls a latch when a fault produces a high current, opening the breaker almost instantly (Lesson 12).
• Lifting magnets: cranes in scrap yards pick up and release steel.
• Motors and generators: coils create the magnetic fields that produce torque or induce voltage.
• Magnetic locks, bells, buzzers and loudspeakers.

Force on a current in a magnetic field

A conductor carrying current in a magnetic field experiences a force, because its own field interacts with the external field. The force is greatest when the conductor is at right angles to the field:

where \(F\) is the force in newtons, \(B\) the flux density in teslas, \(I\) the current in amperes and \(L\) the length of conductor in the field in metres. The direction is given by Fleming's left-hand rule for motors: with the first finger along the field (north to south), the second finger along the current, the thumb points along the force.

This force is the basis of every electric motor. In a DC motor, current flows through coils on the rotating armature in the field of permanent magnets or field windings; the forces on opposite sides of each coil create a torque that turns the shaft. A commutator, a segmented ring with brushes, reverses the current in each coil at the right moment so the torque always acts in the same direction.

Forces between conductors also matter in power systems. During a short circuit, currents of tens of thousands of amperes produce forces large enough to bend busbars and whip cables, which is why switchgear and cable supports are rated for short-circuit forces and why loose conductors in a panel can be dangerous during a fault.

Electromagnetic induction

In 1831, Michael Faraday discovered the reverse effect: a changing magnetic field around a conductor induces a voltage in it. Faraday's law states that the induced voltage in a coil is proportional to the number of turns and the rate of change of flux:

Lenz's law gives the direction: the induced voltage drives a current that opposes the change that produced it. A voltage can be induced by moving a conductor through a field, moving a magnet near a coil, or changing the current in a nearby coil. For a straight conductor moving at right angles through a field, the induced voltage is \(e = B L v\).

Induction is the principle behind:

• Generators: coils rotating in a magnetic field produce AC voltage (Lesson 2).
• Transformers: an alternating current in one coil produces a changing flux in an iron core, inducing a voltage in a second coil; the voltage ratio equals the turns ratio (ELEC-210).
• Induction motors: the changing field of the stator induces currents in the rotor, which then experiences force (ELE-370).
• Current transformers and clamp meters, induction cooktops, wireless chargers and metal detectors.
• Unwanted effects: induced voltages in parallel cables and pipelines, interference, and eddy currents that heat transformer and motor cores (reduced by making cores from thin, insulated laminations).

Magnetic circuits and saturation

Iron can carry only so much flux. As the magnetizing current increases, flux rises steeply at first, then levels off once most of the iron's magnetic domains are aligned: the iron saturates. Beyond saturation, extra current produces little more flux. Motors, transformers and relays are designed to operate below saturation; overvoltage drives them into saturation, causing high magnetizing current and overheating. When iron is magnetized and demagnetized repeatedly (as in AC equipment), some energy is lost in each cycle as hysteresis loss, another reason transformer cores use special low-loss steels.