Magnets and Magnetic Fields

A Magnet attracts certain materials to itself.

A magnet will attract Iron, Steel, Nickel, Cobalt and some alloys of these. A magnet has no noticeable effect on other materials.

A Bar Magnet is strongest at each end.

Dip a bar magnet into iron filings or a box of pins. It attracts the filings or the pins to itself. Most cling on at each end of the magnet.

The regions of greatest strength at each end are called Magnetic Poles.

If a Bar Magnet is suspended freely it will line up approximately North-South.

The pole of the magnet that always points North is called

the North-Seeking Pole or the North Pole.

The pole that points south is called the South-Seeking

Pole or the South Pole.

Magnetic Poles occur in Pairs.

You cannot have a single pole on its own. For every north pole there is always a south pole. The strength of the north pole is the same as the strength of the south pole.

Like poles repel and unlike poles attract

The North Pole of one magnet repels the North Pole of another.

The South Pole of one magnet repels the South Pole of another.

The North Pole of one magnet is attracted to the South Pole of another magnet.

A Magnet causes some materials brought near it or touching it to become magnetised.

This magnetism is called Induced Magnetism. If the magnet is taken away some materials (called permanent magnets) hold on to their magnetism but others (called temporary magnets) lose most of it.

Hard steel holds onto magnetism very well whereas soft iron does not. Ordinary nails are usually made from soft iron and do not retain their magnetism very well.

What is a Magnetic Field?

A Magnetic Field is any region of space where magnetic forces can be felt.

What is the Direction of a Magnetic Field ?

The Direction of the Magnetic Field at a point is the direction of the force on a north pole if it was placed at that point.

What is a Magnetic Field Line?

A line drawn in a magnetic field so that the tangent to it at any point shows the direction of the magnetic field at that point is called a Magnetic Field Line.

What are Magnetic Poles?

Magnetic poles are the regions at each end of a magnet where the magnetic forces are greatest. Magnetic poles are always found in pairs.

If another magnetic field is present it will deflect the compass needle from its N-S position.

If the other field is strong enough the compass needle will line up almost parallel to the field rather than North-South.

A Plotting Compass is a small magnet that can rotate about a vertical axis. If no other magnets are nearby it will line up North-South.

The Magnetic Field around a Bar Magnet

The magnetic field lines start at the north pole and end at the south pole.

The magnetic field lines never cross each other.

Near the poles - where the magnetic field is strongest - the lines are close together. Further away, where the field is weaker, the lines are far apart.

Iron Filings showing the Magnetic Field around a Bar Magnet

The magnetic field around a U-shaped Magnet

Earth’s Magnetic Field, pointing approximately North

As long as the current is flowing the Magnetic Field exists.

If the current stops flowing the Magnetic Field disappears.

What is the Magnetic Effect of an Electric Current?

Every Current-Carrying Conductor has a Magnetic Field around it caused by the current.

Experiment to show the Magnetic Effect of an Electric Current

Set up the equipment with the wire lined up North-South. The plotting compass also lines up N-S.

Close the switch, sending current through the wire. The compass needle will deflect.

Reverse the direction of the current and the needle deflects in the opposite direction.

Open the switch, no current flows, the magnetic field disappears and the compass again lines up N-S.

Conclusion: Every current carrying conductor has a magnetic field around it caused by the current.

The Magnetic Field around a Long Straight Wire

The Right-Hand Grip Rule

If a Right Hand clasps a conductor

with the Thumb pointing in the direction of the Current

Then the Fingers give the direction of the Magnetic Field around the conductor.

The thumb points in the direction of conventional current, i.e. from + to -

A Circular Loop of Wire carries a current in the direction shown.

Using the Right-Hand Grip Rule at a number of points on the wire shows us the shape of the magnetic field around the loop.

The side of the loop facing us behaves like a South Pole (the magnetic field lines are going in)

The other side is like a North Pole (the magnetic field lines are coming out).

The Magnetic Field around a Current-Carrying Coil (or a loop)

The Magnetic Field around a Current-Carrying Solenoid

Electromagnets are used in: Scrap yard cranes Electric motors Electric bells Moving coil loudspeakers Induction coils

By turning the current on or off the magnet can be turned on or off.

By varying the size of the current the strength of the magnet can be varied.

What is an Electromagnet?

A Solenoid carrying a current and containing a soft iron core is known as an Electromagnet.

A powerful Electromagnet lifting scrap Iron

A Magnetic Compass shows the direction of the Earth’s Magnetic Field and it is used in navigation.

The Earth’s Magnetic Field forms a protective layer (from charged particles) around the Earth.

The Magnetic Compass has been used for hundreds of years in marine navigation, since it enables you to know direction. The angle between True North and Magnetic North is also of importance. Charts and maps used in navigation have its value in the locality of the chart noted on them since navigators must allow for it in their calculations.

To show that a Current-Carrying Conductor in a

Magnetic Field experiences a Force

Send a current through the tinfoil.

The foil will move forwards. Reverse the current and the foil will move backwards.

Conclusion: A current-carrying conductor in a magnetic field experiences a force.

The moving coil meter and the moving coil loudspeaker are based on the principle that a current-carrying conductor in a magnetic field experiences a force.

A simple d.c. Motor is based on the principle that a current-carrying conductor in a magnetic field experiences a force.

Why would you expect a current-carrying conductor placed in a magnetic field to experience a force?

A current-carrying conductor has a magnetic field around it due to the current.

When this conductor is placed in another magnetic field, the two magnetic fields interact (push off each other!).

This causes the force on the current-carrying conductor.

What is the Direction of the Force on a Current-Carrying Conductor in a Magnetic Field?

NOTE: A Current-Carrying Conductor in a magnetic field experiences no force if the conductor is parallel to the magnetic field.

The direction of the force is always: Perpendicular to the current

Perpendicular to the magnetic field

Fleming’s Left-Hand Rule: If the thumb, first finger and second finger of the left hand are held at right angles,

with the first finger in the direction of the magnetic field and the second finger in the direction of the current, then the thumb points in the direction of the force.

What determines the Size of the Force on a current-carrying conductor in a magnetic field?

The size of the Current

The Length of the conductor

How strong the Magnetic Field is

The Angle between the conductor and the magnetic field

Magnetic Flux Density (B)

Is the magnitude of the magnetic field strength(B): F I and F l

It follows that: F I l

F = I l B where B is a constant.

The value of B depends on how strong the magnetic field is. In a strong magnetic field B is large and in a weak field B is small. Thus B is a measure of how strong the magnetic field is.

B is called the Magnetic Flux Density.

At a point in a magnetic field the Magnetic Flux Density ( B ) is a vector whose: •direction is the direction of the force on a north pole placed at that point

•magnitude is the value of B from the equation F = I l B

The SI unit of magnetic flux density is the tesla (T)

or put another way:

The magnetic Flux Density (B) at a point in a magnetic field is a vector whose: magnitude is equal to the force that would be experienced by a conductor of length 1 m carrying a current of 1 A at right angles to the field at that point. Its direction is the direction of the force on a north pole placed at that point.

Define Magnetic Flux Density

If the conductor is not perpendicular to the field resolve the B into two perpendicular components - one parallel to the conductor and the other at right angles to the conductor. It is the component of B that is perpendicular to the conductor that causes the force on it. The parallel component has no effect on the wire.

F = B I l Sin 0o

The coil is free to rotate about the axis.

Convince yourself that the directions of the forces on the sides of the coil are correct and that the coil will begin to rotate.

Use the equipment above. The coil is free to rotate about the axis.

When the current is switched on the coil starts to rotate as shown.

To Show the Force on a current-carrying coil in a magnetic field

A beam of electrons in a cathode ray tube moves in a vacuum.

The beam passes close to a fluorescent screen and shows up as a beam of light.

The moving electrons have negative charge and thus are an electric current.

They, therefore, have a magnetic field around them.

A Beam of Electrons in a cathode ray tube is an Electric Current

Force on a Moving Charge in a Magnetic FieldThis magnetic field, due to the beam of moving charges (the electrons), will interact with any other magnetic field placed near it.

The picture shows the beam of electrons deflecting due to the presence of a bar magnet.

The Size of the Force on a Moving Charge in a Magnetic Field

A charge of q coulombs moving with a speed of v metres per second at right angles to a magnetic field of flux density B teslas experiences a force of F newtons, given by;

F = q v B

A charged particle moving at constant speed enters a uniform magnetic field and moves at right angles to the field. Explain why the particle moves in a circle?.

When the charged particle enters the magnetic field there is a force on it.

The force is at right angles to its direction of motion. Therefore its speed does not change. Only its direction of motion changes.

The force on it has a constant magnitude (F = q v B.).

As it turns the force always remains at right angles to the direction of motion.

Thus the particle moves in a circular path.

What is an Electric Current?

What is the SI Unit of electric current?

What is the SI Unit of electric charge?

Define the coulomb.

An Electric Current is a flow of charge.

The ampere (A).

The coulomb (C).

1 coulomb is the amount of charge that passes any point in a circuit when a current of 1 ampere flows for 1 second.

Electric Current and Electric Charge

Electric Current and Electric Charge

What is the relationship between Electric Current and Electric Charge?

The current (I) is the amount of charge (Q) passing per second

Q = I t

Where: Q is charge gone past I is the steady current t is the time taken.

Magnetic Forces between Currents

Two parallel conductors carry current in opposite directions.

Each current creates a magnetic field around itself.

The magnetic fields interact with each other and cause a force on each conductor, pushing the conductors apart.

If the conductors carry current in the same direction the force between them is attractive.

State the principle on which the definition of the ampere is based.

The definition of the ampere is based on the principle that:

Two current carrying conductors exert a force on each other due to their magnetic fields.

The ampere is that current which:

•if maintained in two infinitely long parallel wires, is of negligible cross section

•is placed 1 metre apart in a vacuum

•would produce a force on each wire of 2 × 10-7 newtons per metre of length

The Ampere

What is Magnetic Flux?

Magnetic flux is defined as:

= B A

Where:

= magnetic flux B = magnetic flux density A = area

Magnetic flux through Area A is equal to

Magnetic Flux Density × Area

What is the SI Unit of Magnetic Flux?

The SI Unit of Magnetic Flux is the weber (Wb).

Magnetic flux is a Scalar Quantity.

What is the magnetic flux through a loop of area 0.5 m2 placed at right angles to a magnetic field of flux density 3 T?

= B A

= (3)(0.5)

= 1.5 Wb

B = 3 T

A = 0.5 m2

What if the magnetic field is not perpendicular to the area?

Resolve the magnetic flux density B into components parallel and perpendicular to the area.

Flux through A =

Component of B perp to A × (area A)

In the diagram :

Component of B perp. to coil

= B Sin 30o = 2 Sin 30o = 1 T

Flux through coil = B × A

= (1)(0.4) = 0.4 Wb

What is Electromagnetic Induction?

Whenever the magnetic field passing through a coil changes an emf appears in the coil. This is Electromagnetic Induction.

To Demonstrate Electromagnetic Induction

Move the magnet towards (or away from) the coil.

The galvanometer deflects, indicating that current flows and that an emf appears.

When the magnet is not moving the meter reads zero.

State Faraday’s Law of Electromagnetic Induction.

Faraday’s Law states that the induced emf is directly proportional to the rate of change of magnetic flux.

Taken Time

Flux Initial-Flux FinalE emf Induced Average

Experiment to demonstrate Faraday’s Law of Electromagnetic Induction

Move the magnet towards the coil slowly.

The galvanometer gives a small deflection, indicating a small induced emf.

Move the magnet towards the coil quickly.

The galvanometer gives a large deflection, indicating a large induced emf.

Conclusion: The induced emf is directly proportional to the rate of change of magnetic flux through the coil.

As the man runs towards a coil the magnetic flux through the coil increases. An emf is induced in the coil.

By Lenz's Law the current induced in the coil flows in a direction that opposes the north pole of the magnet approaching.

The current flows in a direction that causes the end of the coil facing the approaching magnet to behave like a north pole (north repels north).

Because of this opposition the man must do work to bring the magnet nearer the coil. The work he does appears as electrical energy in the coil.

As the man runs away from the coil the direction of the induced current changes so that his motion is still opposed.

The direction of the induced current changes so that a south pole appears at the right hand side of the coil (south attracts north).

The work the man does in pulling a north pole away from a south pole again appears as electrical energy in the coil.

State Lenz’s Law.

Lenz’s Law states that the induced current flows in such a direction as to oppose the change causing it.

Lens’s law follows from the Principle of Conservation of Energy.

Experiment to demonstrate Lenz’s LawDrop a metal cylinder through a copper pipe. Note how long it takes to fall through the pipe.

Drop a strong cylindrical magnet (same size and weight as the metal cylinder) through the copper pipe. It takes much longer to fall through.

As the magnet falls through the pipe, its changing magnetic field induces currents in the pipe. By Lenz’s Law these currents flow in such a direction as to oppose the change producing them, i.e the moving magnet. They exert forces on the magnet slowing it down. The non magnetic metal cylinder does not experience these forces

Thus Lenz’s Law is demonstrated.

Hang a light aluminium ring from a piece of thread.

Move the north pole of a bar magnet quickly towards the ring.

The ring moves away from the magnet.

Move the north pole quickly away from the ring and the ring follows the magnet.

Conclusion: As the north pole approaches current is induced in the ring. A north pole appears at the side of the ring nearest the magnet. The magnet repels it and the ring moves away.

When the north pole is taken away the direction of the induced current changes, a south pole appears at the side of the ring facing the magnet. The ring is attracted to the magnet and follows it. This agrees with Lenz’s Law and thus the law is demonstrated.

Experiment to demonstrate Lenz’s Law

An Electric Generator is a device that converts mechanical energy into electrical energy.

The alternator in a car is an electrical generator. This one has a maximum power output of 1 kW.

What is an Electric Generator?

Electric GeneratorsElectromagnetic Induction is the principle on which the Electric Generator is based.

In an electricity generating station some form of energy e.g. chemical energy from coal or oil is used to produce steam which causes a turbine to rotate - i.e. the turbine is given kinetic energy.

The turbine rotates a coil in a magnetic field thereby causing the magnetic flux through it to change and an emf is induced in it.

Thus the kinetic energy is converted to electrical energy.

Everyday examples of Electric Generators

Electricity Power Stations which generate huge quantities of electricity.

The Alternator in a Car is turned by the engine and generates electricity to supply power to the car’s electrical system to continually keep the car battery charged.

The Dynamo on a bicycle generates electricity to operate the bicycle’s lights.

The current that flows through an ordinary domestic light bulb when connected to the mains electricity supply reverses direction 100 times every second.

Mains Electricity is alternating current.

What is alternating Current (a.c.)?

An electric current that periodically reverses the direction in which it flows is called Alternating Current (a.c.).

Alternating Current

A Graph of Current against Time for alternating current

Alternating Voltage

To produce alternating current an alternating voltage is needed.

The diagram shows a graph of an a.c. voltage against time on an oscilloscope.

If alternating voltage is applied across a pure resistor the current flowing at any instant is found from Ohm's Law.

Resistance

instantat that Voltage instant any at Current R

vi

Vo

ltag

e / V

Alternating Voltage

Graph of Voltage against Time for A.C.

3 A d.c. flows in a 6 resistor. Heat is produced in the resistor at a rate given by Joule's Law: P = I 2R = (3)2(6) = 54 J s-1

If Alternating Current flows in the resistor what is the maximum value of the a.c. if it produces heat at the same rate as the 3 A d.c.?

Clearly if the a.c. only reaches 3 A in each direction it will not produce heat at the rate of 54 J s-1, because the current is less than 3 A at all other times in each cycle.

A.C. and Heating

rms Value of an Alternating Current (or Voltage)

When we state that the value of an Alternating Current is 5 A, we mean that this alternating current has the same heating effect as a 5 A direct current.

Since alternating current varies with time, to have the same heating effect as a 5 A d.c. it must have a maximum value in each direction which is greater than 5 A.

The stated value of an alternating current is called its rms value ( symbol Irms ).

The Maximum or Peak Value of the current is symbolised: I0

It can be shown that:

20I

I rms and 20 rmsII

The same thing applies to alternating voltages:

and

20V

Vrms 20 rmsVV

The peak voltage of the mains electricity in Europe is 325 V. Calculate the rms voltage of the mains.

V8.2292

325

20

VVrms

V156211020 rmsVV

Mains voltage is supplied at an rms value of 110 V in the US. Calculate the peak value of the voltage.

Peak voltage (V0) and rms Voltage (Vrms)

What is Mutual Induction?

If a changing electric current in one coil causes an induced emf to appear in a nearby coil there is said to be Mutual Inductance between the two circuits.

How can the amount of Mutual Induction between two coils be increased?

Move the coils nearer each other.

Wind the coils on the same soft Iron core.

Increase the number of turns on either or both of the coils.

Mutual inductance occurs in the Transformer and the Induction Coil.

When the switch S is opened (or closed) the current in coil 1 changes and thus the magnetic field around it changes. This changing magnetic field passes through coil 2.

As this happens the galvanometer in coil 2 gives a deflection showing that an emf is induced in coil 2.

There is thus mutual inductance between the two coils.

Experiment to show Mutual Induction

What is Self Induction?

Whenever the current passing through a coil changes the magnetic field surrounding that coil changes.

This changing magnetic field induces an emf in the coil that opposes the changing current. (This emf is called a back emf ).

This phenomenon is called Self Induction.

Experiment to demonstrate Self Induction

When the switch is closed the bulb does not light immediately. It takes a number of seconds for the bulb to reach full brightness.

This is due to the self inductance of the coil.

Explanation of the Experiment to demonstrate Self Induction

When the switch is closed the current starts to flow and immediately produces a magnetic field around the coil. This field is increasing.

Since the coil now has a changing magnetic field in it, by Faraday's Law an emf will be induced in the coil.

By Lenz's Law the direction of the emf opposes the change producing it, i.e. it opposes the increasing current.

The induced emf opposes but does not succeed in preventing the current from increasing. Such an emf is called a Back emf.

The Effect of an Inductor on a.c.

A 12 V battery sends a 2 A d.c current through a 6 Ω resistor.

If a 12 volt a.c. source (Vrms = 12 V) is connected to a coil of resistance 6 with a soft Iron core in it, current still flows.

However the current that now flows, is much less than 2 A. The reason is:

Alternating current continually changes and so the magnetic field around the coil also changes. By Faraday's and Lenz's Laws an emf is induced in the coil that always opposes the changing current.

It is this back emf that causes the coil to offer more opposition to a.c. than to d.c.

The core causes an increased magnetic flux in the coil and hence a greater rate of change of magnetic flux.

A coil carrying a.c. has a back emf. The greater rate of change of magnetic flux causes the back emf to increase. This reduces the net voltage and the current decreases. The lamp goes out because the current decreases.

A filament lamp lights when connected in series with an a.c. power supply and a coil. Explain why the lamp goes out when a soft Iron core is inserted into the coil.

A coil (an inductor) opposes the flow of direct current (d.c.) with its Ohmic Resistance.

A coil (an inductor) opposes the flow of alternating current (a.c.) with its Ohmic Resistance and the Back emf Induced in it.

A.C. and Inductors

A Dimmer Switch

What is a Transformer?

A Transformer is a device used to change the value of an Alternating Voltage.

Structure of a Transformer

A Transformer consists of two coils of wire wound on a soft Iron core.

One coil, called the Primary Coil has an alternating voltage, called the Input Voltage, applied to it.

The transformer causes a different voltage to appear across other coil, called the Secondary Coil.

The voltage across the secondary coil is the Output Voltage.

How a Transformer Operates

The Input Voltage V i across the primary coil causes alternating current in the primary coil.

This current causes an alternating magnetic flux in the Iron core.

This alternating flux passes through the secondary coil and induces an emf V o in it. V o is the Output Voltage.

The size of the Output Voltage, V o, depends on the number of turns in the secondary N s and N p , the number of turns on the primary coil.

Transformer Formula

s

p

o

i

N

N

V

V

Vi = Input Voltage = Voltage across Primary Coil

Np = Number of Turns on Primary coil

Vo = Output Voltage = Voltage across Secondary Coil

Ns = Number of Turns on Secondary Coil

If Ns is greater than Np then Vo is greater than

Vi and it is called a Step Up Transformer.

If Ns is less than Np then Vo is less than Vi and

it is called a Step Down Transformer.

To Demonstrate the Action of a Transformer

With an a.c. voltmeter measure the voltage across the primary coil and the emf across the secondary coil.

It will be seen that if Ns > Np then Vo > Vi and vice versa.

By noting the number of turns on each coil the formula:can be verified

s

p

o

i

N

N

V

V