Book Reference : Pages 106-107Book Reference : Pages 106-107

1.1. To recap the nature of the magnetic field To recap the nature of the magnetic field around a bar magnet & the Eartharound a bar magnet & the Earth

2.2. To understand the nature of the magnetic To understand the nature of the magnetic field around a current carrying wirefield around a current carrying wire

3.3. To be able to calculate the magnitude & To be able to calculate the magnitude & direction of the force on a current carrying direction of the force on a current carrying wire in a magnetic fieldwire in a magnetic field

DefinitionDefinition : : A magnetic field is a force field which A magnetic field is a force field which surrounds either a magnet or a wire carrying an electric surrounds either a magnet or a wire carrying an electric current and will act upon, without contact, another current and will act upon, without contact, another magnet or current carrying wiremagnet or current carrying wire

Like the other fields we have studied we represent Like the other fields we have studied we represent magnetic fields diagrammatically using field lines or lines magnetic fields diagrammatically using field lines or lines of magnetic fluxof magnetic flux

Plotting Compass

We name the ends of a magnet “the poles”. (North and We name the ends of a magnet “the poles”. (North and & South). More correctly they should be referred to as & South). More correctly they should be referred to as the “North seeking pole” and “South seeking pole”the “North seeking pole” and “South seeking pole”

The arrows on a magnetic field line represent the path The arrows on a magnetic field line represent the path which a “tiny free north pole” would take which a “tiny free north pole” would take

Like poles repel each other

Unlike poles attract each other

The Earth has a The Earth has a magnetic field just magnetic field just like a giant like a giant magnet. magnet.

The geographic The geographic North pole has a North pole has a South magnetic South magnetic pole associated pole associated with it (Since a with it (Since a north seeking pole north seeking pole of a magnet will of a magnet will point towards it)point towards it)

Earth Dipole

Watch terminology!!!Watch terminology!!!

At the geographic At the geographic North pole there is a North pole there is a magnetic pole which magnetic pole which we can refer to as we can refer to as “Magnetic North”. “Magnetic North”. However it is a South However it is a South pole!pole!

Watch the field lines!Watch the field lines!

Wires carrying a magnetic current produce a magnetic Wires carrying a magnetic current produce a magnetic fieldfield

““Maxwell’s corkscrew rule” Maxwell’s corkscrew rule” can be used to establish the can be used to establish the direction of this field. Note the current direction is the direction of this field. Note the current direction is the direction of “conventional current” positive to negativedirection of “conventional current” positive to negative

A current carrying wire, with its associated magnetic A current carrying wire, with its associated magnetic field will experience a “motor effect” if placed (at a non-field will experience a “motor effect” if placed (at a non-zero angle) in a magnetic fieldzero angle) in a magnetic field

The force is perpendicular to both The force is perpendicular to both the current & the magnetic fieldthe current & the magnetic field

Experimentally, it can be shown that the size of the Experimentally, it can be shown that the size of the force due to the motor effect is related to the following :force due to the motor effect is related to the following :

1.1.The strength of the currentThe strength of the current2.2.The strength of the magnetic fieldThe strength of the magnetic field3.3.The length of the wireThe length of the wire4.4.The angle between the field lines & currentThe angle between the field lines & current

In terms of angles, the force is greatest when the current In terms of angles, the force is greatest when the current is perpendicular to the field and zero when parallel to is perpendicular to the field and zero when parallel to the fieldthe field

The relationship between field, current and force can The relationship between field, current and force can best be remembered using “Fleming's left hand rule”best be remembered using “Fleming's left hand rule”

FFirst finger (irst finger (FField), seield), seCCond Finger (ond Finger (CCurrent), urrent), TThumb humb (mo(moTTion)ion)

Expressing the observations as proportionalities :Expressing the observations as proportionalities :

Force Force Current (F Current (F I) I)

Force Force length of wire (F length of wire (F ll) ) (that is a lower case L)(that is a lower case L)

F F I IllFor a given magnetic field we can turn this into an For a given magnetic field we can turn this into an equation whereequation where

F = BIF = BIl l (assuming current is perpendicular to field)(assuming current is perpendicular to field)

Where Where BB is the is the magnetic flux density magnetic flux density and is the force per unit and is the force per unit length, per unit current (N/m/A) but given the unit of length, per unit current (N/m/A) but given the unit of Tesla (T)Tesla (T)

(Note we can introduce a sin (Note we can introduce a sin term to the above equation to consider angle term to the above equation to consider angle but it is beyond our specbut it is beyond our spec

A straight horizontal wire of length 5m is in a uniform A straight horizontal wire of length 5m is in a uniform magnetic field which has a magnetic flux density of magnetic field which has a magnetic flux density of 120mT. The wire is perpendicular to the field lines which 120mT. The wire is perpendicular to the field lines which act due North. When the wire conducts a current of 14A act due North. When the wire conducts a current of 14A from East to West calculate the magnitude and direction from East to West calculate the magnitude and direction of the force on the wireof the force on the wire

Using F = BIUsing F = BIl l F = 120 x 10F = 120 x 10-3-3 x 14 x 5 x 14 x 5

F = 8.4NF = 8.4N

Vertically downwardsVertically downwards

Current East to West

Field due North

a) 2.4x10a) 2.4x10-2-2N West, b) 4.5A east to west, c) 0.2T vertically down, d) N West, b) 4.5A east to west, c) 0.2T vertically down, d) 8.0x108.0x10-3-3 N due south N due south