Chapter 5ELECTRIC FIELD

MAGNETIC FIELDELECTROMAGNETISM

TRANSFORMER

Electric Field

Figure 6.1 represents two parallel metal plates, A and B, charged to different potentials.

Any region in the lines of electric force between the plates in Fig. 6.1, is called an electrostatic field.

Figure 6.2(a) shows a typical field pattern for an isolated point charge, and Fig. 6.2(b) shows the field pattern for adjacent charges of opposite polarity.

Electrostatic field

Electric lines of force (often called electric flux lines) are continuous. It start and finish on point charges; also, the lines cannot cross each other.

V = Supply Voltage (Volt, V)d = Distance between plates (meter, m)A = Area (meter2, m2)

*Electric field strength is also called potential gradient.

Electric Field Strength, E

Electric flux density D is the amount of flux passing through a defined area A that is perpendicular to the direction of the flux

A

*Electric flux density is also called charge density, σ.

Q = Charges (coulombs, C)A = Area (meter2, m2)

Electric Flux Density, D

Example

Exercise

TUTORIAL 1

2

A

Capacitance, CQ = Charges (coulombs, C)V = Volt Applied (Volt, V)

How much charge corresponds to a given p.d. between the plates is the capacitance:

Permittivity, 0 = permittivity of vacuum = 8.85×10−12 F/m.r = relative permittivity (no unit)D = Electric Flux Density (C/m2)E = Electric Field Strenth (v/m)

CONST 32 =Typical values of εr include air, 1.00; polythene,2.3; mica, 3–7; glass, 5–10; water, 80; ceramics, 6–1000.

I = Current (Ampere, A)t = time (seconds, s)

Dielectric

Electrostatic Field established in particular materials

Example

TUTORIAL 1

2

The parallel plate capacitor, C

0 = permittivity of vacuum = 8.85×10−12 F/m.r = relative permittivity (no unit)n = number of plates (no unit)d = distance between plates (meter/m)A = Area (meter2, m2)

Dielectric Strength, Em

Vm = Supply Voltage (Volt, V)d = Distance between plates (meter, m)

Example Exercise1

2

TUTORIAL

12

3

4

Energy stored in capacitors, WV = Voltage Applied(Volt, V)C = Capacitance (Farad, F)

Example

Exercise

TUTORIAL 1

23

Magnetic Field

Magnetic Field

The north-seeking end of the magnet is called the north pole, N, and the south-seeking end the south pole, S. The area around a magnet is called the magnetic field and this field consist of lines of magnetic flux.

In Fig. 7.2(a), with unlike poles adjacent, attraction takes place. But in Fig. 7.2(b), with similar poles adjacent (i.e. two north poles), repulsion occurs.

Magnetic FluxMagnetic flux is the amount of magnetic field (or the number of lines of force) produced by a magnetic source. The symbol for magnetic flux is φ (Greek letter ‘phi’).

The unit of magnetic flux is the weber, Wb. Magnetic flux density is the amount of flux passing through a defined area that is perpendicular to the direction of the flux

Flux Density, B

φ = Magnetic Flux (weber, Wb)A = Area (meter2, m2)

The symbol for magnetic flux density is B. The unit of magnetic flux density is the tesla, T, where 1 T = 1Wb/m2.

Example

Exercise

Magnetomotive force, mmfMagnetomotive force (m.m.f.) is the cause of the existence of a magnetic flux in a magnetic circuit

Magnetic Field StrengthN = Number of turns (No Unit)I = Current (Ampere, A)l = Magnetic Path (Meter, m)

N = Number of turns (No Unit)I = Current (Ampere, A)

Example

Flux, Flux Density & MmfTUTORIAL 1

2

3

4

Electromagnetism

Magnetic field due to an electric current

If a current is now passed through the wire, then the iron filings will forma definite circular field pattern with the wire at the centre. If the current direction is reversed, the direction of the lines of flux is also reversed.

Screw Rule

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.

*screw rule = right hand grip rule

Solenoid

A magnetic field set up by a long coil, or solenoid, is shown in Fig. 8.4(a) and is seen to be similar to that of a bar magnet. If the solenoid is wound on an iron bar, asshown in Fig. 8.4(b), an even stronger magnetic field is produced, the iron becoming magnetised and behaving like a permanent magnet.

Fleming’s left-hand rule

If the current-carrying conductor shown in Fig. 8.3(a) is placed in the magnetic field shown in Fig. 8.13(a), then the two fields interact and cause a force to be exertedon the conductor as shown in Fig. 8.13(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

NS

+_

Fleming’s left-hand rule

MotorWhen current flows in the coil a magnetic field is set up around the coil which 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 downwards between points A and B and upward between C and D for the current direction shown. This causes torque and the coil rotates anticlockwise. When the coil has turned through 90◦ from the position shown in Fig. 8.17 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.

Electromagnetic Induction(a) When the magnet is moved at constant speed towards the coil (Fig. 9.1(a)), a deflection is noted on the galvanometer showing that a current has been produced in the coil.(b) When the magnet is moved at the same speed as in (a) but away from the coil the same deflectionis noted but is in the opposite direction (seeFig. 9.1(b)).(c) When the magnet is held stationary, even within the coil, no deflection is recorded.(d) When the coil is moved at the same speed asin (a) and the magnet held stationary the samegalvanometer deflection is noted.(e) When the relative speed is, say, doubled, thegalvanometer deflection is doubled.(f ) When a stronger magnet is used, a greater galvanometer deflection is noted.(g) When the number of turns of wire of the coilis increased, a greater galvanometer deflection isnoted.

As the magnet is moved towards thecoil, the magnetic flux of the magnet moves across, or cuts, the coil. It is the relative movement of the magnetic flux and the coil that causes an e.m.f. and thus current, to be induced in the coil. This effect is known as electromagnetic induction.

Faraday’s laws• Faraday’s law state that the voltage induced

across a coil of wire equals the number of turns in the coil, multiply the rate of change of the magnetic flux.

Lenz’s laws• Lenz’s law state that when the current

through a coil changes, the polarity of the induced voltage is such it always oppose the change in current.

Fleming’s Right-hand rule

NS

+_

B = Flux Density (Tesla, T)l = Length of conductor in magnetic field (meter, m)v = Conductor movement velocity (ms-1)θ = conductor movement direction towards magnetic field

In a generator, conductors forming an electric circuit are made to move through a magnetic field. By Faraday’s law an e.m.f. is induced in the conductors and thus a source of e.m.f. is created. A generator converts mechanicalenergy into electrical energy.

Induced e.m.f.Example Exercise

TUTORIAL12

Rotation of a loop in a magnetic field

N = Number of turnsB = Flux Density (Tesla, T)l = Length of conductor in magnetic field (meter, m)v = Conductor movement velocity (ms-1)θ = conductor movement direction towards magnetic field

Rotation of a loop in a magnetic fieldExample

Energy stored in inductor, W

I = Current flows (Ampere, I)L = Inductance (Henry, H)

Example TUTORIAL123

Ideal Transformer

Transformer

1

2

2

1

2

1

2

1

II

PP

NN

VV

V1 = Primary VoltageV2 = Secondary Voltage

N1 = Primary TurnsN2 = Secondary Turns

P1 = Primary PowerP2 = Secondary Power

I1 = Primary CurrentI2 = Secondary Current

Transformer 1

2

2

1

2

1

2

1

II

PP

NN

VV

Example Exercise

Transformer

TUTORIAL123

45

6

7

Thank You