Magnetic fields 08

Magnetic Fields

Section 2 Topic 3

Magnetic Fields

Magnetic fields are produced by moving electric charges; hence by electric currents.

In a bar magnet; iron atoms have electrons that spin.

Each spinning electron; tiny ‘magnet’.

Magnetic Fields

As all the electrons spin in the same direction; there is no cancellation, magnetic field is stable.

Field lines can represent magnetic fields; As they did in electric fields.

Magnetic Fields

The drawing of field lines follows the same rules as with electric fields.A compass moved in a magnetic field; follows the field lines.

Field lines follow the direction; North to South.

Bar Magnet B Field

Magnetic Fields

Oersted’s Law

Permanent magnets are not the only source of magnetic fields.Hans Christian Oersted discovered; a magnetic field, around a wire carrying an electric

current.

He showed this by placing compasses around a wire; carrying an electric current.

Oersted’s Law

The field is concentric circles centred on the wire; strongest near the wire.

This magnetic field is in addition to; electric field produced by the

charges.

Oersted’s Law

Oersted’s Law

To determine the direction of the magnetic field around a wire; use Oersted’s right hand rule.

Oersted’s Law

Grab the wire with your right hand,Thumb in the direction of the conventional current, I; (i.e. +ive to -ive),

Field is in the direction of; curl of your fingers.

Oersted's Law

Oersted’s Law

Oersted’s Law

If the wire is shown as vertical; the field is hard to draw, it will be into and out of the page.

Crosses (x) are used to show the field; directed into the page.

Oersted’s Law

Dots () are used to show the field; directed out of the page.

Think of an arrow; when it is flying towards you, see a point (out of the page).

Oersted’s Law

When it is flying away from you; you will see the feathers, cross (into the page).

Oersted’s Law

Oersted’s Law

This concept can also be used to illustrate current. Current flow through a straight wire

Oersted’s LawTo increase the strength of the field increasing the current; the wire can be bent into a loop.

Current flow through a circular coil

Oersted’s Law

To further increase the strength of the field at the centre of the loop; several loops are used instead of the

single wire, to form a flat coil.

Each loop of current carrying wire contributes; to a stronger magnetic field.

Oersted’s LawCurrent flow through a solenoid

Magnetic Force Around a Current-Carrying Conductor

When a current carrying wire is placed in a magnetic field; the two magnetic fields interact.


The two fields are; the permanent field around the

magnet, the field created around the wire.


When the supply is switched on; wire is pushed out until it no longer

touches the mercury, breaks the current, falls back.

It then makes contact again; again is forced out.


This process repeats and the wire; continues to bounce in and out.

This is due to the two interacting magnetic fields producing; a resultant force, at right angles.


This shows that the current; the applied magnetic field, and the force on the wire, mutually perpendicular.

Fleming’s right hand rule shows this.This is also called; right hand palm rule.


The experiment shown above can also be used to show; the force will increase, when any of the following factors

increase:


The current, I, in the wire.The length, l, of the wire.The strength of the external magnetic field (B).


Vector B, the direction of which is the same as the magnetic field lines; describes the strength of the

magnetic field.


Several names are given to B including; magnetic induction, magnetic field intensity, magnetic flux density.


The S.I. units for magnetic induction B are the tesla (T); or weber per square metre (Wbm-2).

The magnetic induction of the Earth’s field; is approx. 10-4 T.


Electromagnets have values; in the order of 2 T;

Superconducting magnets have values; around 10 T.

The relationship between the above quantities is:


F = BIl F is the force on the wire,

in newtons, I is the current flowing in the wire,

in amperes,


B is the magnetic induction of the magnetic field, in tesla,

l is the length of wire in the magnetic field, in metres.


This formula only applies when; wire and the magnetic field is

perpendicular.

If the angle is reduced; force will be reduced.

The formula is more correctly shown by:


F = BIlsin is the angle; between the wire, and the magnetic field.

Note sin is at a maximum when; = 90o, ie when B and I are perpendicular.


The quantity Il is known as; the current element.

Rearranging the formula above; to make B the subject of the

equation:


This leads to the definition of B

lIF

B


The magnitude B of a magnetic field is defined as the force per current element placed at right angles to the field.The direction of magnetic induction is perpendicular to both the force and the current element.


The direction is given by the right hand rule described above.Force is measured in; newtons (N);

Electric current, in amperes (A),


Length of wire, in metres (m),

Magnetic induction, in tesla (T).

1 T = 1 N A-1 m-1.


Try Example 1

Solution

Solution

B = 4.5 T upI = 0.3 A eastl = 2.0 m = 90o

F = BIlsinF = 4.5 x 0.3 x 2 x sin90o

F = 2.7 N

SolutionUse the right hand rule to determine the direction.

Solution

Palm faces out of the page.Direction is southF = 2.7 N south


Try Example 2

Solution

Solution

I = 0.1 Al = 0.1 mg = 9.8 ms-1

m = 2 g = 0.002 kg

Solution

For the wire to be supported against gravity, |FB | = | Fg |

BIl sin = mg

Solution

Use the right hand rule to determine the direction.B = 2.0 T to the right

sinlI

mg

B

1 x 0.1 x 0.1

9.8 x 002.0B

Moving Coil Loudspeaker

The principle of a moving coil loudspeaker is that; a coil carrying an electric current, oscillating with amplitude, and frequency, proportional to the sound to be

produced, is suspended in a uniform magnetic

field.


The magnetic force on the oscillating current; drives the coil in and out, through the field.


A cone is attached to the coil; the movement of the cone back and forth, sets up compressions and rarefactions, in the adjacent air, creating a sound wave.


Motion of LoudspeakerLoudspeaker Animation

Components

Frame (or housing or basket) Stationary Component

Generally an open metal frame; supporting the cone, with a magnetic structure attached, at the centre rear.

Components

Cross section of a Speaker

Components

Components

Magnetic Structure - Stationary ComponentA fixed permanent magnet provides; magnetic field,

in almost all modern designs.

Components

The diagrams above and below show; a ring magnet providing the magnetic

field, with one polarity on each flat face of

the ring.

Components

Magnetic poles are induced in soft iron pole pieces; as shown below.

Resulting in north and south magnetic poles; on opposite sides of a small air gap.

Components

The voice coil moves; in the approximately uniform

magnetic field, in the air gap.

Components

Components

Cone (or diaphragm) Moving Component

Components

A conical surface; made of light but rigid material,

such as paper pulp, or plastic, even Kevlar

that sets the air vibrating.

Components

Voice Coil Moving Component

A coil of wire wound on a lightweight tube; passes through the gap, in the magnetic structure.

Components

The voice coil is attached to the cone; wires from the two ends of the coil

terminate in, electrical connections on the frame.

Aluminium wire is often used; because it is much lighter than

copper.

Components

Inner Suspension or Spider

A flat ring of springy material.The outside edge of the ring is connected to the frame; inside edge is connected to the voice

coil, where it joins the cone.

Components

The purpose of the inner suspension; to hold the cone centrally in the

frame, while allowing it to move in and out

freely, without rocking.

Components

Outer Suspension Moving Component

Performs a similar function to the inner suspension; but between the outer edge of the

cone and the frame.

Components

Centre Cap and Dust Dome Moving Component

Components

Moulded paper or aluminium; covers the centre of the cone at the

end of the voice coil, to prevent dust from entering the

gap, in the magnet assembly.

Components

It also adds to the moving components; acts as an extension of the cone, moving air to create sound.

Action of a Loudspeaker

The two ends of the voice coil are connected; to the output terminals of an

amplifier.

Across the terminals, is a P.D.; oscillates in proportion to the sound

waveform.


This produces an oscillating current in the voice coil.To examine this, we will look at in two stages.The first being when the P.D. is constant.


A constant P.D. gives rise to; a constant I from V = IR.

The magnetic force is determined by; F = BIl.


The direction is determined by the right hand rule.Assume the current is at first, into the page.


The voice coil moves in the direction of; the magnetic force.

The inner and outer suspensions; oppose the motion and, exert a restoring force.


Eventually the forces have equal but opposite magnitude and; the voice coil no longer moves.

The rest position is approximately given by; F = BIl.


As F I and V IF V.If the P.D. is reversed; hence the current.

The force and displacement; are also reversed.


Effect of Changing the CurrentSummary of How it WorksIt appears from above that the P.D. is; proportional to the cone

displacement, therefore is proportional to the sound

waveform.


There are some factors that prevent this from being true.The skill in producing a good speaker is to reduce these factors.These factors, are outside the scope of this course.

Magnetic fields 08

Education

Transcript of Magnetic fields 08