Electricity and Magnetism

• Electrostatics• Electric Current• Magnetism

• Electromagnetism

Electricity and Magnetism

Electrostatics

• It is believed that Thales of Miletus, one of the wise men of ancient Greece, discovered the phenomenon called static electricity. He observed at around 600 B.C. that amber, a fossilized resin attracted tiny particles of wood when rubbed with wool.

Electrostatics

• During the later part of the 15th century, Sir William Gilbert, an English scientist, made a number of experiments to investigate the Properties of loadstones and amber. These started the first systematic study of static electricity. In his book “De Magnete”,published in 1600, he reported his findings and conclusions. He introduced the word “electric” to designate materials which behave like amber.

• Electric Charge- is a basic property of certain elementary particles of which all matter is composed. There are two kinds of electric charge, positive charge and negative charge.

• Electron - negatively charged particles of an atom.

• Proton - positively charged particles of an atom.

Modern plastics can now be used to obtain positive and negative charges. Polythene strip can acquire a negative charge when it is rubbed with a duster. On the other hand, acellulose acetate strip can acquire positive charge using the same duster.

Like charges repel and unlike charges attract

The Electron Theory

When two substances are rubbed together, the electrons are the ones transferred from one substance to the other. Substances became positive when some electrons are removed from them and become negative when some electrons are added to them.

A device to detect the presence of electric charges can facilitate the study of electrostatics.The electroscope is a simple instrument which can do this.

The electroscope consists of a light strip of metal foil or paper hinged to the metal rods or stem. This metal rod is connected to the metal cap or disk and the whole assembly is mounted in a plastic or glass container. This separation of charges when there is a charged material nearby is called electrostatic

induction.

Conductors and Insulators

Conductors allow current to move through it . This indicates that electricity is not possible without them. On the other hand, insulators are also valuable in the sense that they stop charges from flowing from one conductor to another.

Most materials are good conductors because they contain large numbers free electrons per unit volume. Insulators contain practically no free electrons. The electrons in them are tightly bound and normally charge does not flow.

Electrostatic Generator• There are two main types of electrostatic generators

which are traditional items in a physics laboratory. They are the electrophorus and the Van de Graaf generator.

Electrostatic Generators

The electrophorus is a simple electrostatic generator invented by Alessandro Volta.

It has a non-conducting base and a metal plate with an insulated handle. The base acquires a negative charge on being rubbed with fur. When the

metal plate is placed on the base, it is strongly charged by induction. Then grounding will leave the plate charged positively.

Electrostatic Generators

• The Van De Graaf generator is a machine used to charge objects easily. It is capable of producing very high voltage in the order of

10 MV with respect to the ground.

Van De Graaf Generator

Coulomb’s Law

• Charles Coulomb – a French Physicist, made the first quantitative investigation of electric forces with the use of a torsion balance which he invented.

• Coulomb’s Law – states that the force exerted by one charged object on another is proportional to the product of the magnitude of the charges and is inversely proportional to the square of the distance between them.

Sample Problem

1. Find the electric force between two electrons which are separated by a distance of 1mm. The charge of an electron is

1.6 x 10 ⁻¹⁹C.

• Electric Field – is a region around a charged object where any charge placed in it experiences a force which is electrical in nature.

• Electric Field Intensity – is defined as the force per unit charge acting on a charged object placed at that point in the field.

The electric field intensity at a point varies inversely as the square of the distance “r” of the point from Q and directly as the magnitude of the charge.

Sample Problem

2. How much is the electric field intensity at a point 1m away from a charge of

10 x 10⁻⁶C?

Electric Lines of Force

An Electric field can be described visually by drawing lines of electric force. These lines will represent the direction of motion of a small “free” positive charge placed in the field. The density of the lines is used to indicate the intensity of the field. If the charge is positive, the lines of electric force are directed away from it. The lines of electric force is directed towards the charge if it is negative.

Electric Potential and Electric Potential Difference

• Electric potential – work done in bringing charge from a point of zero potential to that point.

• Electric Potential Difference – work done in transferring a charge from one point to another.

• Electron volt – is the energy acquired by an electron that has been accelerated through a potential difference of 1 volt.

Practical Applications of Electrostatics

1. Electrostatic Precipitator2. Fingerprinting3. Xerography4. Paint spraying

Electric Current

• Electric current – rate of flow of electric charges.

• Ampere – unit of electric current in the MKS system. This is equal to a flow of one coulomb of charge per second.

• Andre Marie Ampere – a french mathematician and physicist who formulated some fundamental laws of electricity and magnetism.

Sample Problem

3. How much current is produced if 3.75 x 10²⁰ electrons pass a given point in a conductor in one minute? The charge of an electron is 1.6 x 10⁻¹⁹C.

• Sources of EMF – is any device that will transform non-electrical energy into electrical energy.

• EMF – electromotive force difference in potential between the

electrodes of a source in an open circuit.• Cell – an electron pump• Battery – a device for storing and generating

an electric current by chemical reaction. This is a series of cells.

Electric Circuit

• An electric circuit is the path through which an electric current flows.

Circuit Symbols

Series Circuit

• If we connect 2 or more lamps as shown in the figure, all the electrons that go through 1 lamp must also go to the other lamps.

Parallel Circuit

• If we connect a cell to 2 or more lamps, as shown in this figure, we say that the lamps are connected in parallel. As the electrons reach point N, they divide between the branches of the circuit until they reach point M where they join together again.

Electric Circuit

An instrument which measures the current in a circuit is called an ammeter. It is alwaysconnected in series in the circuit. On the other hand, an instrument which measures potential difference is called a Voltmeter.

Ohm’s Law and Resistance

In 1826, George Simon Ohm, a German physicist, discovered that the current (I) through a metal wire is proportional to the potential difference (V) across it provided that the temperature is kept constant.This relationship is called Ohm’s Law.

This means that the Current (I) is proportional to the voltage or potential difference (V).

In equation form it is V/I = R, where the constant R stands for the resistance of the wire.

We define resistance of a wire as the ratio of potential difference to the current. This definition is actually the Ohm’s Law.

Sample Problem

4. A potential difference of 12V is applied across an electric circuit.

a.) What is the current in the circuit if the resistance is 30 Ohm’s?

b.) If the resistance in the circuit is doubled, what is the current?

Factors Affecting ResistanceThe resistance of a conducting wire that obeys Ohm’s Law depends upon 3 factors:1. The material of which it is made2. The length of the wire3. The cross-sectional area of the wire

It was found that the longer the wire the smaller the current across it.

On the other hand, when the cross-sectional area of a wire is increased, the resistance it offers to the flow of electric charges becomes smaller.

Sample Problem

5. What length of resistance wire of resistivity 100 x 10 ⁻⁸ ohm-m, and of cross-section 2.5 x 10 ⁻⁷ m² would be needed to make a resistor 57.6 ohms?

Superconductors

In 1911, an astonishing discovery was made by M. Kamerlingh Onnes who won a Nobel Prize for it. He found that when mercury is cooled at 4.2°C above absolute zero, its resistance suddenly disappears entirely. The material exhibits the property of superconductivity.

• Superconductors- are materials that lose all resistance when cooled to temperatures near absolute zero. Current once started, flows in them forever.

This indicates that there is no need to replace energy that is lost to resistance if superconductors are used. So superconductors may become the key to tremendous savings of energy and money.

Resistors

A resistor is a device used to introduce resistance into an electrical circuit. Resistors are sometimes made of a length of nichrome wire. Resistors can be used to reduce the current in a circuit.

Resistors and their Circuit Symbol

Resistors in Series

When resistors are in series, the combined resistance is the sum of the individual resistances in the combination and is therefore greater than any individual resistance.

Rт= R₁+R₂+R₃

Sample Problem

6. A potential difference of 6 V is applied to 2 resistors of 8 Ω and 4 Ω connected in series. Find:

a.) The combined resistance of the 2 resistors.

b.) The current flowing in the circuitc.) The potential difference across the

8 Ω resistor.

Resistors in Parallel

When resistors are connected in parallel, the reciprocal of the combined resistance is equal to the sum of the reciprocals of the individual resistances.

1/R= 1/R₁ + 1/R₂ + 1/R₃

Sample Problem

7. A potential difference of 12V is applied to 2 resistors (3Ω and 6Ω) connected in parallel.Calculate:

a.) The combined resistance of the 2 resistors.

b.) The current flowing in the main circuit

c.) The current in the 6Ω resistor

• Power – is defined as the rate of doing work, or the rate at which energy is produced. In simple terms, power is the amount of work done in a unit of time.

Power = Work/ timeP= V IP= I² R

P= V²/ R

Power is measured in joules per second which is called watt.

Sample Problem

8. A burning lamp is marked 22W, 220Va.) How much current flows through the lamp?b.) What is its resistance?

Capacitance

• Capacitance- ratio of electric charge to the potential difference.

Q= CV C = Q/V = 1C/1V = 1 farad

• Capacitor- a device that stores charges.

Sample Problem

9. A parallel-plate capacitor of 10 microfarad capacitance is charged to a potential difference of 5V. How much charge is stored on each plate?

Capacitor images

Magnetism

The term Magnetism comes from the region of Magnesia, an island in the Aegean Sea where certain stones were found by the Greeks more than 2000 years ago. The stones called “ lodestones” had the unusual property of attracting pieces of iron.

Magnets were first fashioned into compasses and used for navigation by the Chinese in the 12th century.

Magnetism

If the north pole of one magnet is brought near the north pole of another magnet, they repel. The same is true of a south pole near another south pole. If opposite poles are brought near each other, attraction occurs. Hence, these observations can be stated as follows:unlike poles attract and like poles repel.

Magnetism

Magnetic poles behave similarly to electric charges in this aspect of attraction and repulsion. But they are very much different in that while an electron and a proton can exist separately, a north pole and a south pole cannot. They always come in pairs.

Broken magnets image

Coulomb’s Law of Magnetism

Coulomb’s law of magnetism states that the force between 2 magnetic poles is directly proportional to the product of their pole strengths and inversely proportional to the square of the distance between them.

Induced Magnetism

If a pole of a magnet is brought to touch one end of the first clip, the second clip can be picked up by the first. This means that the clip which is in contact with the magnet, becomes a magnet itself. We call this phenomenon as induced magnetism.

Magnetic Fields

A magnetic field is a region or space in which a magnet pole placed in it experiences a force which is magnetic in nature. An electric field and a magnetic field have similar characteristics but they are not equivalent.

Magnetic Field

The path taken by an imaginary “free”N- Pole in a magnetic field is called a magnetic line of force or a line of flux.

These flux lines in a magnetic field are collectively called magnetic flux represented by the Greek letter phi Ø. The unit of magnetic flux in MKS System is the Weber. One weber is equal to 10⁸ lines of flux.

Magnetic field around Magnet Combinations

Theory of Magnetism

Theory of Magnetism

Since electron is a charged particle, this theory implies that magnetism is a property of a charge in motion. Two types of electron motion are regarded as important in this concept of magnetism.

First, the revolution of the electron about the nucleus of an atom imparts magnetic property to the structure of the atom.

The second type of motion is the spinning of the electron on its own axis.

How Magnets are Made

• Stroking Method• Electrical Method• By hammering• By heating

Destroying Magnetism

• By hammering• By heating• By Alternating Current Method

Magnetic effect of an Electric Current

In 1813, a Danish Physicist Hans Christian Oersted predicted that a relationship between electricity and magnetism would be found. In 1819, seven years later, Oersted himself discovered that electricity has a magnetic effect. He found that a small compass needle is deflected when brought near a conductor carrying an electric current. This was the first evidence of the suspected relationship between electricity and magnetism.

Oersted Experiment

Forces Between Current-carrying Wires

After Oersted’s discovery of the magnetic effect of an electric current, a French physicist Andre Marie Ampere determined the shape of the magnetic field about a conductor carrying a current. Earlier he had discovered that forces exist between two parallel conductors in a circuit. If the current in the parallel conductors are in the same direction, the two conductors attract one another. The force between the two conductors are repulsive if the currents are in opposite directions.

Magnetic field around a long straight current carrying conductor

As to the determination of the direction of the magnetic field around the conductor, we can make use of the right-hand rule for straight conductors.

The magnitude of the magnetic field B also called as magnetic flux density or magnetic induction, at any point in the magnetic field of a current- carrying conductor is directly proportional to the current in the conductor and inversely proportional to the radial distance, r , of the point from the conductor.

Sample Problem

10. A long straight wire carries a current of 12 A. how much is the magnetic flux density at a point 0.1 meter from the conductor?

Uses of Electromagnets

• In electric Bell and electric Buzzer• In Electromagnetic Relays• In Telephone Earpiece and in Radio Earphone

Force on a Current-carrying Conductor in a Magnetic field

The force on the wire depends upon the strengths of the 2 magnetic fields. Thus, a force may be increased by increasing the current in the wire and by increasing the strength of the uniform field.

Fleming’s Left-hand Rulestates that if the thumb, forefinger and the

middle finger of the left hand are held at right angles to each other, then the forefinger points in the direction of the magnetic field, the center finger points in the direction of the conventional current and the thumb points in the direction of the force on the wire.

Electromagnetic Induction

In 1831, Michael Faraday discovered how to make electricity using magnetism. He found out that an electromotive force is set up in a conductor located in a magnetic field, when the magnetic flux is cut by the conductor. Joseph Henry, at about the same time made a similar discovery.

Electromagnetic Induction- current is induced in the wire, if the wire is moved to cut across lines of force

Fleming’s Right-hand Rule

states that if your right-hand is held in a fist and thumb, the forefinger and the middle finger are spread out at right angles to each other, the forefinger points in the direction of the magnetic field, the thumb points in the direction of the movement of the wire and the middle finger points in the direction of the induced current.

Fleming’s Right-hand Rule

Simple Generator

• An electric generator converts mechanical energy into electrical energy. The essential components of a generator are a field magnet, an armature, slip rings, and brushes.

AC Generator

• In a n AC Generator, the current is conducted in and out by way of slip-rings and carbon brushes. A current that reverses to and fro like this is what we call Alternating Current.

DC Generator

• It has a splitring commutator so that the current in the brush contact always flows in the same way.

Transformer

Transformer is a device used to covert voltage from low to high ( step-up ) or from high to low ( step-down ).