chapter 7 magnetic fields. 7.1 the creation of magnetic fields

Chapter 7Magnetic Fields

7.1 THE CREATION OF MAGNETIC FIELDS

Creation of magnetic fields

• All moving electric charges create magnetic fields

• This magnetic field is separate from, and in addition to, the electric field associated with these charges

• Stationary electric charges have no magnetic field, only an electric field

Creation of magnetic fields

7.2PICTORIAL REPRESENTATION OF MAGNETIC FIELDS

The field of a Bar Magnet

• The direction of a magnetic field is from the North pole of the magnet to the South pole, as indicated by arrows on the field lines

• Magnetic field lines always form closed loops

The field of a Bar Magnet

• The direction of the field at any point is in a direction that is at a tangent to the field line at any point

• The magnitude of a magnetic field at any point is represented by the density of the magnetic field lines at that point

General representation of Magnetic Fields

• The magnetic field is a vector, it has magnitude and direction

• In the case of bar magnets and other magnetostatic examples (unchanging magnets) there is a North and South pole

• However magnetic fields created by electric currents do not have this property

General representation of Magnetic Fields

• In both gravitational and electric fields, the filed lines are lines of force:

– The direction of field lines for a gravitational field is the direction of force on a mass at that point in the field

– The direction of field lines for an electric field is the direction of force on a positive charge at that point in the field

General representation of Magnetic Fields

• The direction of the magnetic field is the direction of force on the North pole of a magnetic dipole placed at that point

General representation of Magnetic Fields

Class problems

Conceptual questions: 1-6

7.3SOME SPECIFIC MAGNETIC FIELDS

The Earth’s magnetic field• The direction of magnetic field lines is the direction

of force on the North pole of a compass

• This means that the North pole of the Earth is actually the South pole of the Earth's magnetic field

Conventional Current

• When electric currents were first investigated, it wasn’t known that current flow was movement of positive or negative charge

• It was assumed that electric current was the flow of positive charge

Conventional Current

• Rather than change all electrical theory when electrons were discovered, the term conventional current was created as the flow of positive charge

• Whenever the term current is used, it refers to conventional current – the flow of positive charge – unless specifically stated as electron current flow

The Magnetic Field of a Straight Current Carrying Conductor

• The magnetic field of a straight wire carrying an electric current is circular as shown below

The Magnetic Field of a Straight Current Carrying Conductor

• A current directed into the page is represented by a cross, a current out of the page is represented by a distinct dot

The Magnetic Field of a Straight Current Carrying Conductor

• The magnetic field lines become more widely spaced as they move away from the wire, this shows the field getting weaker

Direction of Magnetic Fields – The Right Hand Curl Rule

• The direction of magnetic field around a current carrying wire can be found using the right hand (curl) rule

• Hold the wire with the right hand, with your thumb pointing in the direction of the conventional current

• The direction of your fingers wrapped around the wire indicate the direction of the magnetic field

Direction of Magnetic Fields – The Right Hand Curl Rule

Magnetic Field of a Current Loop

• If the wire forms a loop, we can still apply the right hand rule as shown below

Magnetic Field of a Current Loop

• It can be seen from the diagram that the magnetic field vector is always pointing in the same direction, in this case it is directed upwards through the loop

Magnetic Field of a Current Loop

• The magnetic field lines join up to form closed loops, and the magnetic field within the wire loop is approximately uniform

Magnetic Field of a Solenoid

• A solenoid is a continuous wire wound around a cylindrical core

• It can be considered to be many loops stacked together

Magnetic Field of a Solenoid

• The current in all of the loops is travelling in the same direction

• This means the resultant magnetic field of all the loops link up to produce the resultant field shown

Magnetic Field of a Solenoid

• For a solenoid with a very large number of coils, the magnetic field inside the solenoid is considered to be almost uniform

Magnetic Field of a Solenoid

• Solenoids are used to create powerful electromagnets, a soft iron core is used to greatly amplify the magnetic field

Magnetic Field of a Solenoid

• When the current is switched off, the field disappears, and the iron core loses its magnetism

Right hand solenoid rule

• Hold the solenoid in the right hand with the fingers wrapped around it in the direction of the current

• The outstretched thumb gives the directions of the North pole of the solenoid

Class problems

Conceptual questions: 9-12

Descriptive questions: 2-3, 5

7.4MAGNETIC FIELD STRENGTH

Magnetic Interactions

• When two magnetic fields come into contact, they interact and forces of attraction and repulsion can occur

Magnetic Interactions

• We can determine the strength of the fields by the magnitude of force they exert on objects placed in them

Forces & field strengths

• The gravitational field strength is defined as the force per unit mass on a mass placed in the field

• The electric field strength is defined as the force per unit charge on a positive charge at that point

Forces & field strengths

• If a current carrying wire is placed in a magnetic field, the force depends on four separate quantities, not just two like gravitational and electric fields:

– The strength of the magnetic field– The magnitude of the electric current– The length of the current (wire) in the field– The orientation (direction) of the current with respect to

the magnetic field

Forces & field strengths• The force on a current carrying wire is maximum

when the current element (wire of length, Δl, carrying a current, I) is at right angles to the magnetic field

• The magnitude of magnetic field strength is the force per unit current element placed at right angles to the field at that point in the field

The Magnetic Field Vector B

• B is the magnetic field strength in Tesla (T)

1T = 1 NA-1.m-1

• F is force in Newtons• I is the magnitude of the current in Amperes• Δl is the length of the wire in the magnetic field in metres

Class problems

Conceptual questions: 14, 16-17

Descriptive questions: 6, 8, 9

7.5MAGNETIC FORCE ON A CURRENT CARRYING CONDUCTOR

Magnetic force on an electric current• When considering the magnetic force on an electric

current placed in a magnetic field we need to consider 3 different situations:

– When the current is perpendicular to the magnetic field

– When the current is parallel to the magnetic field

– When the current is flowing at some angle θ to the magnetic field (0<θ<90°)

Force on a Current Perpendicular to the Magnetic field

• Magnitude of magnetic field strength was defined using a current element perpendicular to the magnetic field

• Rearranging the relation for Force gives:

F = IΔlB

Force on a Current Perpendicular to the Magnetic field

• In the diagram below, the left hand shows a wire with no current in a uniform magnetic field

• It doesn’t interact with the field and therefore doesn’t experience a force

Force on a Current Perpendicular to the Magnetic field

• On the right side, the wire is carrying a current which generates a magnetic field

• Since magnetic field lines cannot cross, they get compressed, which results in a force on the wire

Force on a Current Perpendicular to the Magnetic field

• If the direction of the magnetic field is reversed, the direction of the force is reversed

• If the direction of the current is reversed, the direction of the force is reversed

Force on a Current Perpendicular to the Magnetic field

• The direction of the force can be found using the right hand palm rule as illustrated below:

Force on a Current Parallel to the Magnetic field

• When the current is parallel to the field as in the diagram below, the two magnetic field create perpendicular field lines

• The perpendicular fields do not interact, therefore no force is generated

Force on a Current at an Angle θ to the Magnetic field

• The current in the wire can be considered as a vector IΔl, with its direction being in the direction of the current I

• Thus it can be resolved into two components, one perpendicular and one parallel to the magnetic field

Force on a Current at an Angle θ to the Magnetic field

• The parallel component does not interact with the uniform field, only the perpendicular component is subject to a force

• This can be given by:

F = IΔlB sinθ

Force on a Current at an Angle θ to the Magnetic field

• This is the general formula for currents in a magnetic field since:

– When the current is parallel to the field, θ = 0° or 180°, hence sinθ = 0 and hence F = 0

– When the current is perpendicular to the field, θ = 90°, hence sinθ = 1 and hence F = IΔlB

Class problems

Conceptual questions: 17

Descriptive questions: 9

Computational questions: 1-6

7.6APPLICATION:THE MOVING COIL LOUDSPEAKER

How sound is produced

• Sound waves are periodic sequences of:– Compressions (regions of high density compressed air)– Rarefactions (regions of low density rarefied air)

How sound is produced

• The number of vibrations per second determines the frequency of the sound, higher frequencies give a higher pitch sound

Low Frequency High Frequency

Construction of a moving coil loudspeaker

• The diagram below shows the parts of a moving coil loudspeaker

Construction of a moving coil loudspeaker

• Frame: Supports the cone and magnet structure, usually an open metal frame

Construction of a moving coil loudspeaker

• Magnet structure: A fixed permanent ring magnet provides the magnetic field, magnetic poles are induced in the soft iron pole pieces

Construction of a moving coil loudspeaker

• Cone: A conical surface made from light but rigid material (paper pulp, plastic, Kevlar, etc) that vibrates, generating sound waves

Construction of a moving coil loudspeaker

• Coil: A coil of wire (often aluminium) that passes through the gap in the magnet structure, and is attached to the cone

Construction of a moving coil loudspeaker

• Inner suspension: A ring of flat springy material attached to the frame that holds the cone and coil central

Construction of a moving coil loudspeaker

• Outer suspension: performs a similar function to the inner suspension at the outer edge of the cone

Construction of a moving coil loudspeaker

• Centre cap & dust dome: Molded plastic or aluminium covering the centre of the cone to add rigidity and keep dust out of the magnet assembly

Woofers and tweeters

• The cone loudspeaker is good for a large range of frequencies, but does not produce higher frequencies as well due to the inertia and internal vibrations of the cone

• This is overcome in high quality systems by using a dome driver, which doesn’t have a cone, to produce higher frequencies

Action of a moving coil loudspeaker

• When a potential difference is applied to the coil, it generates a constant current, given by I = ΔV/R, since the resistance (R) is also constant

Action of a moving coil loudspeaker

• This current generates a magnetic force on the coil in the field given by F = IlB

Action of a moving coil loudspeaker

• I is the current in the coil, l is the length of the coil (circumference multiplied by the number of turns, and B is the magnetic field strength (constant)

Class problems

Conceptual questions: 18

Descriptive questions: 10, 12, 14

Computational questions: 9, 12, 14, 16-17