ElectricityElectricityAC -Alternating currentAC -Alternating current

Magnetic fieldsMagnetic fields

All magnets are dipolar- That is they have All magnets are dipolar- That is they have a north and a south polea north and a south pole

N

SN S

Magnetic fieldsMagnetic fields

Like poles repel each other Like poles repel each other Unlike poles attractUnlike poles attract

NS NS

NS N S

Attract

Repel

Magnetic fieldsMagnetic fields

Like poles repel each other Like poles repel each other Unlike poles attractUnlike poles attract

NS NS

NS N S

Attract

Repel

Magnetic fieldsMagnetic fields

Like poles repel each other Like poles repel each other Unlike poles attractUnlike poles attract

NS NS

NS N S

Attract

Repel

Magnetic fieldsMagnetic fields

Like poles repel each other Like poles repel each other Unlike poles attractUnlike poles attract

NS NS

N N S

Attract

Repel

Field around magnets Top N-S Bottom N-N

Field around Earth

Magnetic fieldsMagnetic fields

A piece of unmagnetised iron will have A piece of unmagnetised iron will have magnetism magnetism inducedinduced in it when it is placed in it when it is placed in an external magnetic field.in an external magnetic field.

NS IronS N

As a result the magnet attracts the Iron

Magnetic fieldsMagnetic fields

The direction of a magnetic field at a The direction of a magnetic field at a particular point in the field is the same as particular point in the field is the same as the force that would act on an imaginary the force that would act on an imaginary single north pole placed at that point.single north pole placed at that point.

NS

Magnetic fieldsMagnetic fields

When a magnet is placed in a magnetic When a magnet is placed in a magnetic field the magnetic forces causes it to align field the magnetic forces causes it to align with that field. The north end of the with that field. The north end of the magnet pointing in the direction of the fieldmagnet pointing in the direction of the field

NS

Direction of the field

Magnetic fieldsMagnetic fields

The strength of a magnetic field is called The strength of a magnetic field is called its magnetic field strength and is given the its magnetic field strength and is given the symbol symbol . It is a vector quantity having . It is a vector quantity having both strength and direction.both strength and direction.

Magnetic fieldsMagnetic fields

It is a measure of the force acting on an It is a measure of the force acting on an imaginary north pole placed at a point in a imaginary north pole placed at a point in a magnetic field. We will consider the unit for magnetic field. We will consider the unit for magnetic field later. But remember a magnetic field later. But remember a vector must be added or subtracted vector must be added or subtracted vectoriallyvectorially

Magnetic fieldsMagnetic fields

B1

B2

BR = B1 + B2

Vector Addition

Vector Subtraction: Reverse the second vector and add

B1

BR = B1 - B2

-B2

Current in a wireCurrent in a wire

When a current flows in a wire a magneticfield is produced around the wire.The direction of this field is determined byA rule called the right hand screw rule

Right hand screw ruleRight hand screw rule

Grasp the wirein the right handwith the thumb pointing in the direction of conventional current (+ -> -)Your fingers indicate the direction of the field around the wire

Current in two parallel wiresCurrent in two parallel wires

When we pass a current through two wiresThat are parallel to each other we find that a force acts between them. The direction of this force is given by the right hand palm rule

Right hand palm ruleRight hand palm rule

Orient your right hand so that your thumb points in the direction of conventional currentAnd your finger(held straight points in the direction of the magnetic field, Then the direction of the force is the direction your palm is pointing

i

F

RememberRemember

Right hand screw rule determines the direction of a magnetic field around a current carrying Wire.Right hand palm rule determines the direction of a force acting on a current carrying wirein a magnetic field

ProblemProblem

Determine the Determine the direction of the force direction of the force acting between two acting between two wires if wires if

a.a. the current flows in the current flows in the same directionthe same direction

b.b. The current flows in The current flows in opposite directionsopposite directions

Same DirectionSame Direction

RH grip rule to determineDiection of field

Right palm rule to find forceThumb upFingers into pagePalm points left

F

B i

Same DirectionSame Direction

RH grip rule to determineDiection of field

Right palm rule to find forceThumb upFingers out of pagePalm points right

F

B

i

Hence wires arr attractedTo each other

Opposite DirectionOpposite Direction

RH grip rule to determineDiection of field

Right palm rule to find forceThumb upFingers into pagePalm points left

F

Bi

Opposite DirectionOpposite Direction

RH grip rule to determineDiection of field

Right palm rule to find forceThumb downFingers out of pagePalm points right

F

B

i

Hence wires are repelledby each other

Magnetic forceMagnetic force

The size of the magnetic force acting on a currrent carrying wire in a magnetic fieldis found using the formula

F = Bil

Where F = Force in newtons i = current in amps

l = length of wire B = Magnetic field strength in Tesla

Magnetic field strengthMagnetic field strength

Magnetic field strength is measured in TeslaThe Tesla is defined as the force experienced by a wire 1m in lengthcarrying a current of 1 amp1 Tesla = 1 Newton per amp.meterThe Tesla is often divided into smaller unitsMilliTesla(10-3) and microTesla(10-6)An older unit is the gauss = 10-4 Tesla

Magnetic field strengthMagnetic field strength

TeslaNeutron star 108

Man made 560Very strong 20Magnetic storm on sun 1Alnico magnets 0.01Earths surface 5 x 10-5

Interstellar space 10-10

Smallest value in shielded room 10-14

Magnetic forceMagnetic force

In the equationF = Bil

F = B and l are all vectors and if they are not at right angles to each other we need to consider the angle between them.

F = Bil sin

Magnetic forceMagnetic force

i

B

F out of the page

F = Bilsin

Magnetic forceMagnetic force

= 0

i B

F = Bilsin = Bilsin 0 = Bil x 0 = 0

When the wire is parallel to the field = 0

Magnetic forceMagnetic force

Force is a maximum when the current is at Force is a maximum when the current is at right angles to the field. F = Bilright angles to the field. F = Bil

Force is zero when the current is parallel Force is zero when the current is parallel to the fieldto the field

Force is equal to Bil sin Force is equal to Bil sin where where is the is the angle between B and the current flow angle between B and the current flow

ProblemProblemDetermine the magnitude of the magnetic Force, due to the earths magnetic field, on 100m of suspended power line running east west and carrying 100AAnswer Field is right angles to the current F = Bil = 5 x 10-5 x 100 x 100 = 0.5 N

ProblemProblemDetermine the magnitude of the magnetic Force, due to the earths magnetic field, on 100m of suspended power line running North South and carrying 100AAnswer Field is parallel to the current F = Bil sin 0 = 0 N

ProblemProblemDetermine the magnitude of the magnetic Force, due to the earths magnetic field, on 100m of suspended power line running North east to South west and carrying 100AAnswer Field is 45 to the current F = Bil sin 45 = 5 x 10-5 x 100 x 100 sin45 N

= 0.5 x sin45 =0.3536 N

ProblemProblemDetermine the magnitude of the magnetic Force, due to the earths magnetic field, on 100m of suspended power line running North South but with a dip angle of 40and carrying 100AAnswer Field is parallel to the current F = Bil sin 0 =5 x 10-5 x 100 x 100 sin40 N

= 0.5 x sin40 = 0.32 N

SolenoidsSolenoidsMagnets and atomsMagnets and atoms

The field around a straight wire is circular.

If we bend the wire

If we bend the wire

xx

xx

x x x xx

x

x

xxxxxxxx

xx

xx

xX field into page

. Field out of page

So the field inside the loop is out of the pageWhile the field outside the loop is into the page

xx

xx

x x x xx

x

x

xxxxxxxx

xx

xx

xX field into page

. Field out of page

SolenoidSolenoid

This means we geta North pole to the leftAnd south to the right

These poles are more obvious with more turns

So a series of loops would result in a north and a south end. Such series is called a soleniod and the field around it is the same as for a magnet.

The Right hand solenoid rule is used to determine which end of a solenoid is the north end and which the south end.Grasp the solenoid in your right hand with your finger in the direction of the current. Your thumb points to North.

N

The Right hand solenoid rule is used to determine which end of a solenoid is the north end and which the south end.Grasp the solenoid in your right hand with your finger in the direction of the current. Your thumb points to North.

N

NN

Any magnetic field that has a north and south pole is called a dipole fieldThe field around a wire is not a dipole and is called a non dipole fieldFields around solenoids are dipole fields

The magnetic field created by an electric current is called an electro magnetic field.If a soft iron core is placed inside a solenoid it increases the magnetic field 1000 fold

If an iron core is placed inside a solenoid while it is on it becomesa magnet.In the same way if a piece of iron is stroked with a magnet it becomes a magnet.

Force on moving chargesForce on moving charges

When an electric charge is placed in a When an electric charge is placed in a magnetic field the field has no effect on magnetic field the field has no effect on the charge.the charge.

Once the charge moves in the magnetic Once the charge moves in the magnetic field it experiences a force. So the force on field it experiences a force. So the force on an electric current is actually the force on an electric current is actually the force on moving electric chargesmoving electric charges

Force on moving chargesForce on moving charges

The size of this force depends on the size of the The size of this force depends on the size of the charge q, the speed of the charge v and on the charge q, the speed of the charge v and on the magnetic field strength Bmagnetic field strength B

F = Bqv F = Bqv where F is perpendicular to v and v is where F is perpendicular to v and v is

perpendicular to perpendicular to Where v and B are not a right anglesWhere v and B are not a right angles

F = Bqv sinF = Bqv sinWhere Where is the angle between v and B is the angle between v and B

The direction of the force is again The direction of the force is again determined from the RH palm ruledetermined from the RH palm rule

Where the thumb is the direction the Where the thumb is the direction the charge is moving( + to -) , The fingers are charge is moving( + to -) , The fingers are in the direction of the magnetic field and in the direction of the magnetic field and the palm is in the direction of the force.the palm is in the direction of the force.

ELECTRIC MOTORSELECTRIC MOTORS

Electric motorsElectric motors

An electric motor relies on the magnetic An electric motor relies on the magnetic force in a current carrying loop in a force in a current carrying loop in a magnetic fieldmagnetic field

Electric motorElectric motor

To increase the power we increase the number of To increase the power we increase the number of loops in the coil this increases the power of the loops in the coil this increases the power of the motor many foldmotor many fold

F = n x BilF = n x BilWe also introduce a commutator so that we have a We also introduce a commutator so that we have a

smother current flowing in many coils giving a smother current flowing in many coils giving a more consistant power out of the motormore consistant power out of the motor

The coil is also wrapped around a soft iron core The coil is also wrapped around a soft iron core increasing the magnetic field strength by 1000 increasing the magnetic field strength by 1000 foldfold

ProblemProblem

A coil in the form of 4 cm squares consists of 20 turns and A coil in the form of 4 cm squares consists of 20 turns and carries 5 amps in a field of 0.8 tesla.carries 5 amps in a field of 0.8 tesla.

What is the force on each side of the coil?What is the force on each side of the coil?

Answer F = n x BilAnswer F = n x Bil

= 20 x 0.8 x 5 x .04= 20 x 0.8 x 5 x .04

= 3.2 N= 3.2 N