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Electricity and Magnetism

Chapter: Electricity and Magnetism

Electric charge

Electric charge also called electricity comes from batteries and generators. Some materials get charged when they are rubbed. Their charge is called electrostatic charge or static electricity. It causes sparks when you take off a pullover and it may even give a shock.

Negative and positive charges

Polythene and Perspex can be charged by rubbing them with a dry, woolen cloth. When two charged polythene rods are brought close together they repel.  The same thing happens with two charged Perspex rods. However a charged polythene rod and a charged Perspex rod attract each other. This experiment suggest that there are two different and opposite charges. These are called positive and negative charge.

Like charges repel; unlike charges attract. The closer the charges, the greater the force between them.

Where charges come from

Everything is made up of tiny particles called atoms. These have electric charges inside them. Atom consists of central nucleus made up of protons and neutrons. Electrons possess a negative charge and protons have an equal positive charge. Neutrons have nil charge.

Generally atoms have equal number of electrons and protons so the overall charge on a material is zero. But when tow materials are rubbed together electrons may be transferred from one to the other. One material ends up with more electrons than normal and the other with less. Hence one has a net negative charge and the other is left with a net positive charge. We can say that rubbing material together does not make electric charge but just separate charges that are already there.

Conductors and insulators

When some materials gain charge they lose it almost immediately. This happens because electrons flow through them or the surrounding material until the balance of negative and positive charge is restored.

Conductors are materials that let electrons pass through them. Metals are termed to be the best electrical conductors. Some electrons of the metals are so loosely held to their atoms and so they can pass freely between them. These free electrons make metals good thermal conductors. Most non-metals except carbon, conduct charge poorly or they do not conduct at all.

Insulators are materials that hardly conduct at all. Their electrons are firmly held to atoms and are not allowed free to move. They can be transferred by rubbing.

Semiconductors are in-between materials. They are poor conductors when cold but they are better conductors when they are warm.

Earthing

If adequate charge build up on something electrons may be pulled through the air and cause sparks which can be dangerous. The objects can be earthed to prevent charge building up. They can be connected to the ground by a conducting material so that the unwanted charge flows away.

Induced charges

Charges that appear on an uncharged object because of a charged object are called induced charges.

Unit of charge

The SI unit of charge is the coulomb(C). It is equivalent to the charge on about 6 million million million electrons though it is not defined in this way. One coulomb is a fairly large quantity of charge. Generally it is convenient to measure charge in micro coulombs.

1 micro coulomb (µC) = 10-6C (one millionth of a coulomb)

Using electrostatic charge

Electrostatic precipitators

These are fitted to the chimneys of some power stations and factories. They cut down pollution by removing tiny bits of ash from the waste gases. In the precipitator, ash is charged by wires and then attracted to the metal plates by an opposite charge. The ash collects in the tray at the bottom when shaken from the plates.

Industrial inkjet printers

These are used for printing lettering on the boxes. It uses the force between charges to control where the ink drops go.

Photocopiers

A light sensitive plate is given a negative charge inside the photo copier. An image of the original document is projected onto the plate. The bright areas lose their charge but the dark areas keep it. Powdered ink called toner is attracted to the charged areas. Then a blank sheet of paper is pressed against the plate and picks up powdered ink. The paper is heated so the powdered ink melts and sticks to it. Thus a copy of the original document is obtained.

Electric fields

The electric charges are said to be in an electric field if they feel a force. In the diagram below, lines with arrows on them are used to represent electric fields.

 

 

 

The arrows show the direction in which the force on a positive charge (+) charge would act. As like charges repel, the field lines always points away from positive (+) charge and towards negative (-) charge.

When a conductor is charged up, the charges repel each other so they collect on the outside. The charges are most concentrated near the sharpest curve.  Here the electric field is strongest and the field lines closest together.

Ions are electrically charged atoms or group of atoms. Atoms become ions if they lose electrons. A stream of ions is a flow of charge.

Current in a simple circuit

An electric cell which is commonly called a battery can make electrons move when there is a conductor connecting its two terminals. Then the chemical reactions inside the cell push electrons from the negative terminal round to the positive terminal.

The cell above is being used to light a bulb. The filament is heated up as the electrons flow through the bulb. So the bulb glows. The conducting path through the bulb, wires, switch and battery is called a circuit. There must be complete circuit for the electrons to flow. Turning the switch OFF breaks the circuit and stops the flow.

Measuring current

A flow of charge is called an electric current. The higher the current, the greater the flow of charge. The SI unit of current is the ampere (A). An ammeter is a device used to measure electric current in a circuit. 1A = 1000 mA.

There is a link between charge and current.

            Charge = current x time

Potential difference

The source of electricity is of two charges, positive and negative. The amount of charge on a body is measured in coulomb and is symbolized as C. These charged particles flow in a particular direction and they need some potential difference to move as they don’t move on their own.

Electric potential difference (PD) is defined as the work done to move a unit charge from one point to the other. It is generally called voltage.

Mathematically it is expressed as

Potential difference (V) = Work Done (W)/Charge (q)

V = W/q

The SI unit of electric potential difference is Volt.

The maximum PD is called the electromotive force (EMF) of the cell. Voltmeter is used to measure potential difference. And a voltmeter is always connected in parallel across the points between which the potential difference is to be measured.

Cells in series

Several cells are connected in series to produce higher PD.

Resistance

There must be voltage across it for making a current flow through a conductor.  The electrical resistance of a conductor is defined as the opposition to the flow of an electric current through that conductor.

R= PD across conductor (V) /Current through conductor (A)

The unit of resistance is called the ohm and its symbol is Ω.

Some factors affecting resistance

There are several factors on which resistance of a conductor depends:

1. Length

Doubling the length of a wire doubles its resistance.

2. Cross-sectional area

Halving the end on area of a wire doubles its resistance. So a thin wire has more resistance than a thick one.

3. Material

A nichrome wire has more resistance than copper wire of the same size.

4. Temperature

Resistance increases with temperature for metal conductors. It decreases for semiconductors.

There is a heating effect whenever a current flows through a resistance. This principle is used in heating elements and also in light bulbs with filaments. The heating effect occurs because electrons collide with atoms as they pass through a conductor.

Resistance components

  1. Resistors are specially made to provide resistance. It reduces the current in a circuit.
  2. Variable resistors (rheostats) are used for varying current.
  3. Thermistors have a high resistance when cold but a much lower resistance when hot. They contain semiconductor materials.
  4. Light-dependent resistors (LDRs) have high resistance in the dark but low resistance in the light.
  5. Diodes have an extremely high resistance in one direction but a low resistance in the other. Hence they allow current to flow in one direction only.

V, I, R equations

The resistance can be written using symbols:

R= V/I where R = resistance, V = PD (voltage) and I = current

The above equation can be rearranged as

V = IR and I = V/R

Ohm’s Law

Ohm’s law explains the relation between potential difference and the current through a conductor.

The current (I) is proportional to the potential difference (V). The slope of the line gives the value of the resistance R. This relationship, between potential difference and current, was first established by the German Physicist, George Simon Ohm and is known as Ohm’s law.

The current through a conductor element is proportional to the potential difference applied between its ends, provided the temperature remains constant. If the voltage V is applied to an element and a current ‘I’ is passes through it,

V α I

V/I = constant

= R

(Or) V = RI

Here R is a constant for the given metallic wire at a given temperature and is called its resistance.

The effects of length and area on resistance

The twice the length, the twice will be the resistance.

                                     Resistance α length

 And if twice the cross sectional area, it will have half the resistance.

                                                             Resistance α 1 / area

Hence we can combine the above and say that for any given conducting material at constant temperature,   

                                   Resistance α length / area.

Series and parallel circuits

There are two methods of connecting the resistors together.

  1. Resistors in series
  2. Resistors in parallel

Let us discuss about each of the above in detailed.

Resistors in Series

Two or more resistors are said to be connected in series if the current flowing through one also flows through the others. You will find that the value of the current is the same everywhere in the circuit. So, in a series connection, the same current passes through the resistors.

And the potential difference V is the sum of potential differences V1, V2 and V3.

Therefore, V = V1 + V2 + V3

Applying Ohm’s law V = IR, we get V1 = IR1, V2 = IR2, V3 = IR3. Therefore, Rs = R1 + R2 + R3

We can conclude that when several resistors are joined in series, the equivalent resistance of the combination Rs equals the sum of their individual resistances, R1, R2, R3, and is also greater than any individual resistance

Resistors in Parallel

If resistors are connected in such a way that the same potential difference gets applied across each of them, they are said to be connected in parallel.

You will find that the current I gets divided into the branches such that

I = I1 + I2 + I3

 The total current flowing into the combination is equal to the sum of the currents passing through the individual resistors.

The currents I1, I2, I3 through the resistors R1, R2, R3 by Ohm’s law as,

Since the resistors are in parallel,

I = I1 + I2 + I3

Substituting the value of currents in the above equation,

V/Req = V/R1 + V/R2 + V/R3

Thus, 1/Req = 1/R1 + 1/R2 + 1/R3

Similarly, if there are n resistors connected in parallel their equivalent resistance Req is given by

1/Req = 1/R1 + 1/R2 + 1/R3 +…………+ 1/Rn

For two resistances R1 and R2 connected in parallel

1/Req = 1/R1+ 1/R2 =(R1+R2)/R1R2

Req = R1R2/(R1+R2)

Electrical power

Electric power is the rate of consumption of energy. In simple terms, it denotes the rate at which electric energy is dissipated or consumed in an electric circuit.

The power is given by

Power = energy transformed / time taken

The SI unit of electric power is Watt (W). It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. The unit ‘watt’ is very small. In daily life, we use a much larger unit called ‘kilowatt’. It is equal to 1000 watts.

Electrical power equation

The power is given by

Power = PD X Current

P = VI

But PD = current x resistance

So power = current x resistance x current

Power = current2 x resistance

In symbols,      P= I2R

We can see that doubling the current produces four times the power dissipation.

Mains electricity

Mains current is alternating current.  It flows backwards and forwards, backwards and forwards… 50 times per second in some countries. The mains frequency is 50 hertz (Hz). In other countries the mains frequency is 60 HZ. AC is easier to generate than one-way direct current (DC) like that from a battery.

The supply voltage depends on the country. For household circuits, some countries use a voltage on the range 220-240V, others in the range 110-130V.

Live wire

This goes alternately negative positive, making the current flow backwards and forwards through the circuit.

Neutral wire

This completes the circuit. In many systems, it is kept at zero voltage by the electricity supply company.

Switch

This is fitted in the live wire. It would work equally well in the neutral but wire in the cable would still be live with the switch OFF. This would be dangerous if the cable was accidentally cut.

Fuse

This is a thin piece of wire which overheats and melts if the current is too high.

Earth wire

This is a safety wire. It connects the metal body of the kettle to earth and stops it becoming live.

Double insulation

Some appliances do not have an earth wire. This is because their outer case is made of plastic rather than metal. The plastic acts as an extra layer of insulation around the wires.

Plugs

Plugs are a safe and simple way of connecting appliances to the mains.

Circuit breaker

A circuit breaker is an automatic switch which trips when the current rises above the specified value. It can be reset by turning the switch on or by pressing a button.

Safety first

Mains electricity can be dangerous. Here are some of the hazards.

  1. Old, frayed wiring. When a current flows through it, the heating effect may be sufficient to melt the insulation and cause a fire.
  2. Long extension leads. These may overheat if used when coiled up. The current makes the wire warm, but the heat has less area to escape from a tight bundle.
  3. Water in sockets or plugs. Water will conduct a current, so if electrical equipment gets wet, there is risk that someone might be electrocuted.
  4. Accidentally cutting cables.

If an accident happens and someone is electrocuted, you must switch off at the socket and pull out the plug before giving any help.

Electrical energy equations

Energy transformed = power x time

But power = PD x Current

Therefore the above equation becomes

Energy transformed = PD x current x time

In symbols, E= VIt

Energy transformed is actually measure in Joules.

Electricity supply companies use the kilowatt-hour rather than joule as their unit of energy measurement.

Calculating the cost of electricity

The electricity meter in a house is an energy meter. The more energy you take, the more you have to pay. The reading on the meter gives the total energy supplied in Units. The unit is another name for the kilowatt hour.

 

Magnetims

Magnetic poles

If a small bar magnet is dipped into iron filings, the filings are attracted to its ends. The magnetic force seems to come from the two points called the poles of the magnet.

The Earth exerts forces on the poles of a magnet. If a bar magnet is suspended, it swings around until it lies roughly north-south. This effect is used to name the two poles of a magnet. These are called the north-seeking pole (the N pole) and the south-seeking pole (the S pole).

Like poles repel; unlike poles attract. The closer the poles, the greater the force between them.

Induced magnetism

Materials such as iron and steel are attracted to magnets because they themselves become magnetized when there is a magnet nearby. The magnet induces magnetism in them. The induced pole nearest the magnet is the opposite of the pole at the end of the magnet. The attraction between unlike poles holds each piece of metal to the magnet. The steel and the iron behave differently when pulled right away from the magnet. The steel keeps some if it is induced magnetism and becomes a permanent magnet. However the iron loses virtually all of its induced magnetism. It was only a temporary magnet.

Making a magnet

A piece of steel becomes permanently magnetized when placed near a magnet, but its magnetism is usually weak. It can be magnetized more strongly by stroking it with one end of a magnet.

Magnetic and non-magnetic materials

A magnetic material is one which can be magnetized and is attracted to magnets. All strongly magnetic materials contain iron, nickel or cobalt. Steel is mainly iron. Strong magnetic materials like this are called ferromagnetic.

Hard magnetic materials such as steel and alloys called Alcomax and Magnadur are difficult to magnetize but do not readily lose their magnetism. They are used for permanent magnets.

Soft magnetic materials such as iron are relatively used to magnetize, but their magnetism is only temporary. They are used in the cores of electromagnets and transformers because their magnetic effect can be switched on or off or reversed easily.

Non-magnetic materials include metals such as brass, copper, zinc, tin and aluminium as well as non-metals.

Where magnetism comes from

In an atom, tiny electrical particles called electrons move around a central nucleus. Each electron has a magnetic effect as it spins and orbits the nucleus. In an unmagnetized material, the atomic magnets point in random directions. But as the material becomes magnetized, more and more of its atomic magnets line up with each other.

If a magnet is hammered, its atomic magnets are thrown out of line; it becomes demagnetized. Also heating it to a high temperature has the same effect.

Magnetic fields

Magnetic fields can be investigated using a small compass. We can observe that when a compass is brought near a current carrying wire/ conductor the needle of compass deflects. The deflection is because of flow of electricity. This proves that electric current produces a magnetic effect.

Magnetic field is the influence of force which is surrounding a magnet. This force exerted by the magnet can be detected by a compass or a magnet.

Field lines are the imaginary lines of magnetic field around a magnet. Let us consider an experiment. Get some iron filings and place around a magnet. They get arranged in a pattern which depicts the magnetic lines.  Magnetic field is a vector quantity. It has both magnitude and direction.

Direction of Field Line:

The direction of magnetic field line outside the magnet is considered from North Pole to South Pole. And inside the magnet, the direction is considered from South Pole to North Pole.

Strength of magnetic field: 

The closer lines show stronger magnetic field and vice versa. 

The Earth’s magnetic field

The earth has a magnetic field. The Earth’s magnetic S pole is the magnetic north. And the magnetic south is the Earth’s magnetic N pole. Magnetic north is over 1200 km away from the Earth’s geographic North Pole.

Magnetic effect of a current

Magnetic field around a wire

If an electric current I passed through a wire, a weak magnetic field is produced. The field has the following features:

  1. The magnetic field lines are circles
  2. The field is strongest close to the wire
  3. The strength of the field increases as the current increases

A rule for field direction

The direction of the magnetic field produced by a current is given by the right hand grip rule shown above. Let us hold a current carrying conductor in your right hand in such a way that the thumb is pointing towards the direction of current. Then the direction of magnetic lines is the direction in which our fingers wrapped around the conductor.  This is called as Right hand thumb rule.

Magnetic Field in a Solenoid

Solenoid is defined as the coil with many circular turns of insulated copper wire and they are wrapped closely in the shape of cylinder.

A current carrying solenoid produces same pattern as of magnetic field as a bar magnet. One end of solenoid behaves as the North Pole and the other end behaves as the South Pole. Magnetic field lines are actually parallel inside the solenoid; similar to a bar magnet. It shows that inside a solenoid, magnetic field is same at all points.

Magnetic materials can be magnetized, by producing a strong magnetic field inside the solenoid. Such a magnet formed by producing magnetic field inside a solenoid is called electromagnet.

Electromagnets

An electro magnet can be switched on and off unlike an ordinary magnet. In a simple electromagnet a coil consisting of several hundred turns of insulated copper wire is wound round a core usually of iron.  When a current flows through the coil, it produces a magnetic field.

The strength of the magnetic field is increased by:

  1. Increasing the current
  2. Increasing the number of turns in the coil

Reversing the current reverses the direction of the magnetic field.

The magnetic relay

A magnetic relay is a switch operated by an electromagnet. With a relay, a switch within thin wires can be used to turn on the current in a much more powerful circuit.

The circuit breaker

A circuit breaker is an automatic switch which cuts off the current in a circuit if this rises above a specified value. It has similar effect as a fuse except that it can be reset after it has tripped which is not possible in a fuse.

Magnetic force on a current

Copper is non-magnetic, so it feels no force from the magnet. But when current passes through it, there is a force on the wire. The force arises because the current produces its own magnetic field which acts on the poles of the magnet.

The force is increased if:

  1. The current is increases
  2. A stronger magnet is used
  3. There is increase in the length of wire in the field.

Fleming’s left hand rule

If the left hand is stretched in such a way that the index finger, middle finger and thumb are in mutually perpendicular direction, then the index finger shows the direction of magnetic field and the middle finger shows the direction of electric current.

Devices such as electric motor, electric generator, etc works on this principle.

Electric motors

Electric motor is a device which converts electrical energy into mechanical energy. It works on Fleming’s left hand rule.

A rectangular coil is suspended between the two poles of a magnet and the electric supply is connected with the help of a commutator. Commutator is defined as a device which reverses the direction of flow of electric current through a circuit

When electric current is supplied to the coil of electric motor, the coil gets deflected because of magnetic field. When it reaches the half way, the split ring acts as commutator and reverses the direction of flow of electric current. The direction of forces acting on the coil also reverses because of the reversal of direction of current. The change in direction of force pushes the coil; and it moves another half turn. Hence the coil completes one rotation around the axle. This process keeps on continuing to keep the motor in rotation.

Electromagnetic Induction

The process in which electric current is generated by varying magnetic fields is appropriately called electromagnetic induction.

This phenomenon is studied by Michael faraday.

Let us explain in the following way. Let us see that a conductor is moved inside a magnetic field and hence electric current is induced in the conductor. A potential difference is induced in conductor when it is brought into relative motion with a magnetic field. This is called as electromagnetic induction. Scientifically speaking, an EMF is induced in the wire. This can be detected by a meter called a galvanometer.

Electromagnetic induction can be explained by Fleming’s right hand rule. If the right hand is stretched in such a way that the index finger, middle finger and thumb are in mutually perpendicular direction, then the thumb shows the direction of movement of the conductor,  the index finger shows the direction of magnetic field and the middle finger shows the direction of induced electric current in the conductor.

Electromagnetic induction is used in the transfer of kinetic energy into electrical energy.

The EMF induced in a conductor is proportional to the rate at which magnetic field lines are cut by the conductor.

The induced EMF can be increased by:

  1. Moving the magnet faster
  2. Using a stronger magnet
  3. Increasing the number of turns on the coil 

Induced current direction: Lenz’s law

If a magnet is moved in or out of a coil, a current is induced in the coil. The direction of this current can be predicted using Lenz’s law.

An induced current always flows in a direction such that it opposes the change which produced it.

Induced current direction: Fleming’s right-hand rule

If a straight wire is moving at right angles to a magnetic field, the direction of the induced current can be found using Fleming’s right hand rule.

When a current causes movement, the left-hand rule applies.

When motion causes a current, the right-hand rule applies.

Eddy currents

If the aluminium disc is set spinning, it may be many seconds before frictional force finally brings it to rest. However, if it is spinning between the poles of a magnet, it stops almost immediately. This is because the disc is a good conductor and currents are induced in it as it moves through the magnetic field. These are called eddy currents.

Generators

It is similar to that of electric motor.

A rectangular armature is placed within the magnetic field of a permanent magnet. Armature is a soft iron core with large number of conducting wire turns over it. The armature is attached to wire and is placed in such a way that it can move around an axle. An electric current is induced when the armature moves within the magnetic field. The direction of induced current starts changing when the armature crosses the halfway mark of its rotation. Thus, the direction of current changes once in every rotation. Because of this, the electric generator generally produces alternate current, i.e. AC.  A split ring commutator is used to convert an AC generator into a DC generator. This produces direct current. A device called rectifier changes its AC output to DC.

AC – Alternate current:

Current in which direction is changed periodically is called Alternate Current. Most of the power stations generate alternate current in many countries.

DC – Direct current:

Direct current is the current that flows in one direction only. Electrochemical cells make direct current.

Coils and transformers

A moving magnetic field can induce an EMF (voltage) in a conductor. A changing magnetic field can have the same effect.

Mutual induction

When coils are magnetically linked so that a changing current in one causes an induced EMF in the other, this is called mutual induction.

A simple transformer

Ac voltages can be increased or decreased by using a transformer. It works by the principle of mutual induction. When alternating current flows through the primary coil it sets up an alternating magnetic field in the core and in the secondary coil. This changing field induces an alternating voltage in the output coil.

Step-up and step-down transformers

Depending on its turns-ratio, a transformer can increase or decrease an AC voltage.

Step-up transformers

They have more turns on the output coil than on the input coil, so their output voltage is more than the input voltage. Large step-up transformers are used in power stations to increase the voltage to the levels needed for overhead power lines.

Step-down transformers

They have fewer turns on the output coil than on the input coil, so the output voltage is less than the input voltage. In battery chargers, computers, and other electronic equipment, they reduce the voltage of the AC mains to much lower levels needed for other circuits.

Both types of transformer work on AC, but not on DC. Unless there is a changing current in the input coil, no voltage is induced in the output coil.

Power through a transformer

If no energy is wasted in a transformer, the power delivered by the output coil will be the same as the power supplied to the input coil. So:

            Input voltage x   input current   = output voltage   x   output current

It means a transformer which increases the voltage will reduce the current in the same proportion and vice versa.

Power across the country

Power for the AC mains is generated in power stations, transmitted through long-distance cables and then distributed to consumers.

A large power station might contain four generators each producing a current of 20000 amperes at a voltage of 33000 volts. The current from each generator is fed to a huge step-up transformer which transfers power to overhead cables at a greatly increased voltage. The cables feed power to a nationwide supply network called a grid. Using the grid, power stations in areas where the demand is low, can be used to supply areas where the demand is high.

Power from the grid is distributed by a series of substations. These contain step-down transformers which reduce the voltage in stages to the level needed by the consumers.