# Electromagnetism

### Magnetic Field due to an Electric Current

Magnetic fields can be set up not only by permanent magnets, as shown in chapter 45, but also by electric currents.

Let a piece of wire be arranged to pass vertically through a horizontal sheet of cardboard on which is placed some iron filings, as shown in Figure 47.1(a). If a current is now passed through the wire, then the iron filings will form a definite circular field pattern with the wire at the centre, when the cardboard is gently tapped. By placing a compass in different positions the lines of flux are seen to have a definite direction as shown in Figure 47.1(b). If the current direction is reversed, the direction of the lines of flux is also reversed. The effect on both the iron filings and the compass needle disappears when the current is switched off. The electric current thus produces the magnetic field. The magnetic flux produced has the same properties as the flux produced by a permanent magnet. If the current is increased the strength of the field increases and, as for the permanent magnet, the field strength decreases as we move away from the current-carrying conductor.

In Figure 47.1, the effect of only a small part of the magnetic field is shown. If the whole length of the conductor is similarly investigated it is found that the magnetic field round a straight conductor is in the form of concentric cylinders as shown in Figure 47.2, the field direction depending on the direction of the current flow.

When dealing with magnetic fields formed by electric current it is usual to portray the effect as shown in Figure 47.3. The convention adopted is:

(i) Current flowing away from the viewer, i.e. into the paper, is indicated by Ð. This may be thought of as the feathered end of the shaft of an arrow. See Figure 47.3(a)

(ii) Current flowing towards the viewer, i.e. out of the paper, is indicated by This may be thought of as the point of an arrow. See Figure 47.3(b).

The direction of the magnetic lines of flux is best remembered by the screw rule which states that:

If a normal right-hand thread screw is screwed along the conductor in the direction of the current, the direction of rotation of the screw is in the direction of the magnetic field.

For example, with current flowing away from the viewer (Figure 47.3(a)) a right-hand thread screw driven into the paper has to be rotated clockwise. Hence the direction of the magnetic field is clockwise.

A magnetic field set up by a long coil, or solenoid, is shown in Figure 47.4(a) and is seen to be similar to that of a bar magnet. If the solenoid is wound on an iron bar, as shown in Figure 47.4(b), an even stronger magnetic field is produced, the iron becoming magnetised and behaving like a permanent magnet. The direction of the magnetic field produced by the current I in the solenoid may be found by either of two methods, i.e. the screw rule or the grip rule.

(a) The screw rule states that if a normal right-hand thread screw is placed along the axis of the solenoid and is screwed in the direction of the current it moves in the direction of the magnetic field inside the solenoid. The direction of the magnetic field inside the solenoid is from south to north. Thus in Figures 47.4(a) and (b) the north pole is to the right.

(b) The grip rule states that if the coil is gripped with the right hand, with the fingers pointing in the direction of the current, then the thumb, outstretched parallel to the axis of the solenoid, points in the direction of the magnetic field inside the solenoid.

#### Electromagnets

The solenoid is very important in electromagnetic theory since the magnetic field inside the solenoid is practically uniform for a particular current, and is also versatile, in as much that a variation of the current can alter the strength of the magnetic field. An electromagnet, based on the solenoid, provides the basis of many items of electrical equipment, examples of which include electric bells, relays, lifting magnets and telephone receivers.

##### (i) Electric bell

There are various types of electric bell, including the single-stroke bell, the trembler bell, the buzzer and a continuously ringing bell, but all depend on the attraction exerted by an electromagnet on a soft iron armature. A typical single stroke bell circuit is shown in Figure 47.5. When the push button is operated a current passes through the coil. Since the iron-cored coil is energised the soft iron armature is attracted to the electromagnet. The armature also carries a striker that hits the gong. When the circuit is broken the coil becomes demagnetised and the spring steel strip pulls the armature back to its original position. The striker will only operate when the push is operated.

##### (ii) Relay

A relay is similar to an electric bell except that contacts are opened or closed by operation instead of a gong being struck. A typical simple relay is shown

in Figure 47.6, which consists of a coil wound on a soft iron core. When the coil is energised the hinged soft iron armature is attracted to the electromagnet and pushes against two fixed contacts so that they are connected together, thus closing some other electrical circuit.

##### (iii) Lifting magnet

Lifting magnets, incorporating large electromagnets, are used in iron and steel works for lifting scrap metal. A typical robust lifting magnet, capable of

exerting large attractive forces, is shown in the elevation and plan view of Figure 47.7 where a coil, C, is wound round a central core, P, of the iron casting. Over the face of the electromagnet is placed a protective non-magnetic sheet of material, R. The load, Q, which must be of magnetic material is lifted when the coils are energised, the magnetic flux paths, M, being shown by the broken lines.

##### (iv) Telephone receiver

Whereas a transmitter or microphone changes sound waves into correspond- ing electrical signals, a telephone receiver converts the electrical waves back into sound waves. A typical telephone receiver is shown in Figure 47.8 and consists of a permanent magnet with coils wound on its poles. A thin, flexible diaphragm of magnetic material is held in position near to the magnetic poles but not touching them. Variation in current from the transmitter varies the magnetic field and the diaphragm consequently vibrates. The vibration produces sound variations corresponding to those transmitted.

Force on a Current-carrying Conductor

If a current-carrying conductor is placed in a magnetic field produced by per- manent magnets, then the fields due to the current-carrying conductor and the permanent magnets interact and cause a force to be exerted on the conductor. The force on the current-carrying conductor in a magnetic field depends upon:

(a) the flux density of the field, B teslas

(b) the strength of the current, I amperes,

(c) the length of the conductor perpendicular to the magnetic field, l metres, and

(d) the directions of the field and the current.

When the magnetic field, the current and the conductor are mutually at right angles then:

Force F = BIl newtons

When the conductor and the field are at an angle g° to each other then:

Force F = Bil sin newtons

Since when the magnetic field, current and conductor are mutually at right angles, F D BIl, the magnetic flux density B may be defined by B D Il , i.e., the flux density is 1 T if the force exerted on 1 m of a conductor when the conductor carries a current of 1 A is 1 N.

For example, a conductor carries a current of 20 A and is at right angles to a magnetic field having a flux density of 0.9 T. If the length of the conductor in the field is 30 cm, the force acting on the conductor is given by:

F D BIl D ˛0.9)˛20)˛0.30) D 5.4 N when the conductor is at right angles to the field, as shown in Figure 47.9(a)

When the conductor is inclined at 30° to the field, as shown in Figure 47.9(b), then

##### Loudspeaker

A simple application of the above force is the moving coil loudspeaker. The loudspeaker is used to convert electrical signals into sound waves.

Figure 47.10 shows a typical loudspeaker having a magnetic circuit com- prising a permanent magnet and soft iron pole pieces so that a strong magnetic field is available in the short cylindrical air gap. A moving coil, called the voice or speech coil, is suspended from the end of a paper or plastic cone so that it lies in the gap. When an electric current flows through the coil it produces a force that tends to move the cone backwards and forwards according to the direction of the current. The cone acts as a piston, transferring this force to the air, and producing the required sound waves.

If the current-carrying conductor shown in Figure 47.3(a) is placed in the magnetic field shown in Figure 47.11(a), then the two fields interact and cause a force to be exerted on the conductor as shown in Figure 47.11(b). The field is strengthened above the conductor and weakened below, thus tending to move the conductor downwards. This is the basic principle of operation of the electric motor and the moving-coil instrument.

The direction of the force exerted on a conductor can be pre-determined by using Fleming’s left-hand rule (often called the motor rule) which states:

Let the thumb, first finger and second finger of the left hand be extended such that they are all at right angles to each other, (as shown in Figure 47.12). If the first finger points in the direction of the magnetic field, the second finger points in the direction of the current, then the thumb will point in the direction of the motion of the conductor.

Summarising:

#### Principle of Operation of a Simple d.c. Motor

A rectangular coil that is free to rotate about a fixed axis is shown placed inside a magnetic field produced by permanent magnets in Figure 47.13. A direct current is fed into the coil via carbon brushes bearing on a commutator, which consists of a metal ring split into two halves separated by insulation. When current flows in the coil a magnetic field is set up around the coil that interacts with the magnetic field produced by the magnets. This causes a force F to be exerted on the current-carrying conductor, which, by Fleming’s left- hand rule, is downward between points A and B and upward between C and D for the current direction shown. This causes a torque and the coil rotates anticlockwise. When the coil has turned through 90° from the position shown in Figure 47.13 the brushes connected to the positive and negative terminals

of the supply make contact with different halves of the commutator ring, thus reversing the direction of the current flow in the conductor. If the current is not reversed and the coil rotates past this position the forces acting on it change direction and it rotates in the opposite direction thus never making more than half a revolution. The current direction is reversed every time the coil swings through the vertical position and thus the coil rotates anti-clockwise for as long as the current flows. This is the principle of operation of a d.c. motor which is thus a device that takes in electrical energy and converts it into mechanical energy.

#### Principle of Operation of a Moving-coil Instrument

A moving-coil instrument operates on the motor principle. When a conductor carrying current is placed in a magnetic field, a force F is exerted on the conductor, given by F D BIl. If the flux density B is made constant (by using permanent magnets) and the conductor is a fixed length (say, a coil) then the force will depend only on the current flowing in the conductor.

In a moving-coil instrument a coil is placed centrally in the gap between shaped pole pieces as shown by the front elevation in Figure 47.14(a). (The air-gap is kept as small as possible, although for clarity it is shown exaggerated in Figure 47.14). Steel pivots, resting in jewel bearings, on a cylindrical iron core, support the coil. Current is led into and out of the coil by two phosphor bronze spiral hairsprings which are wound in opposite directions to minimise the effect of temperature change and to limit the coil swing (i.e. to control the

movement) and return the movement to zero position when no current flows. Current flowing in the coil produces forces as shown in Figure 47.14(b), the directions being obtained by Fleming’s left-hand rule. The two forces, FA and FB, produce a torque that will move the coil in a clockwise direction, i.e. move the pointer from left to right. Since force is proportional to current the scale is linear.

When the aluminium frame, on which the coil is wound, is rotated between the poles of the magnet, small currents (called eddy currents) are induced into the frame, and this provides automatically the necessary damping of the system due to the reluctance of the former to move within the magnetic field.

The moving-coil instrument will measure only direct current or voltage and the terminals are marked positive and negative to ensure that the current passes through the coil in the correct direction to deflect the pointer ‘up the scale’. The range of this sensitive instrument is extended by using shunts and multipliers (see Chapter 50)

#### Force on a Charge

When a charge of Q coulombs is moving at a velocity of v m/s in a magnetic field of flux density B teslas, the charge moving perpendicular to the field, then the magnitude of the force F exerted on the charge is given by: