Section v 22 Electromagnetism

7/28/2019 Section v 22 Electromagnetism

1/19

Electromagnetism22. Electromagnetism

Content

22.1 Force on a current-carrying conductor

22.2 Force on a moving charge

22.3 Magnetic fields due to currents

22.4 Force between current-carrying conductorsLearning Outcomes

Candidates should be able to:

(a) show an appreciation that a force might act on a current-carrying conductorplaced in a magnetic field.

(b) recall and solve problems using the equation F = BIlsin, with directions asinterpreted by Fleming's left-hand rule.

(c) define magnetic flux density and the tesla.

(d) show an understanding of how the force on a current-carrying conductor canbe used to measure the flux density of a magnetic field using a currentbalance.


2/19

(e) predict the direction of the force on a charge moving in a magnetic field.

(f) recall and solve problems using F = BQvsin.

(g) sketch flux patterns due to a long straight wire, a flat circular coil and a long

solenoid.

(h) show an understanding that the field due to a solenoid may be influenced bythe presence of a ferrous core.

(i) explain the forces between current-carrying conductors and predict thedirection of the forces.

(j) describe and compare the forces on mass, charge and current in gravitational,

electric and magnetic fields, as appropriate.


3/19

3

Electromagnets

An electromagnet is a coil which can produce a magnetic field when a

current passes through it

Electromagnets are temporary magnets formed due to the flow of current

through the material.

The strength of an electromagnet can be increased by

Increasing the current

Increasing the number of turns ie length of conductor

The use of a soft-iron core


4/19

4

Action at a Distance Explained

Although two magnets may

not be touching, they still

interact through their

magnetic fields.

This explains the actionat a distance, say of a

compass.


5/19

5

Physics of electromagnets

A ferromagnetic material is characterized by numerous tiny crystals each of which

has one or more domains.

An elementary magnet resides in each domain. In the un-magnetized state, theelementary magnets are arranged randomly.

When subjected to a magnetic field, the elementary magnets line up with the

external field.

Strong exchange forces now bind the elementary magnets together within each

domain. Because they are all parallel, they give rise to a very strong field.

When a current is passed through a coil wound round a ferromagnetic material, it

sets up a magnetic field tending to align the elementary magnets in the domains inthe same direction resulting in a stronger field making it into an electromagnet


6/19

6

Uses of electromagnets

Electric bells

Electromagnetic relays

Telephone earpiece

Electromagnetic crane

Factory robots

Cassette recorders

Magnetic levitation trains


7/19

The motor effect

If a conductor is placed between magnetic poles and a current is passedthrough the conductor, the magnetic fields of the current carrying conductorand the magnet may interact causing forces between them

The existence of force can be demonstrated with an apparatus like on pg 321fig 12.18 Physics by Chris Mee where a strip of aluminium foil is held looselybetween the poles of a horseshoe magnet so that the foil is at right angles to

the magnetic field

When the current is switched on, the foil jumps and becomes taut showingthat a force is acting on it. This force is known as the electromotive forceand the direction of the force depends on the directions of the magnetic fieldand of the current

This phenomenon is known as the motor effect or the catapult effect


8/19

8

Direction of the force on a current carryingconductor in a magnetic field

When a current carrying wire is placed in a magnetic field, a force will act onthe wire, causing the wire to move or to turn

Direction of the force acting on the wire can be determined using Fleming'sleft-hand rule

Fleming's LH Rule

First finger is the direction of the magnetic field

Second finger points in the direction of the current

Thumb shall point in the direction of the force ormotion


9/19

Magnitude of the force on a current carryingconductor in a magnetic field - Current balance

The magnitude of the electromotive force may be determined or investigatedusing a current balance pg 322 fig 12.20 Physics by Chris Mee

Variation of current Ileads to the conclusion that the electromotive force isdirectly proportional to the current

Variation of the length of the wire L in the magnetic field leads to the

conclusion that the electromotive force is proportional to the length of the wirein the magnetic field

By varying the angle bewteen the wire and the direction of the magnetic field,the force is found to be proportional to sin

Hence F IL sin leading to F = BIL sin where B is a constant whichdepends on the strength of the magnet. The stronger the magnet the greaterthe value of B

For a long straight conductor carrying unit current at right angles to a uniformmagnetic field, the magnetic field strength B is numerically equal to the forceper unit length of the conductor in the field ie F/L = BI sin


10/19

Magnetic field strength and tesla

Magnetic field strength B is usually referred to as magnetic flux density which ismeasured in SI unit oftesla (T)

An alternative name for magnetic field strength is the weber per square metre, Wbm-2

One tesla is defined as the uniform magntic flux density which acting normally to a

long straight wire carrying a current of 1 ampere, causes a force per unit length of 1 Nm-1 on the conductor

Since on rearranging, B = F/(ILsin ) , the tesla may also be expressed as N m-1 A-1

Since B involves a force which is a vector quantity, hence magnetic flux density is alsoa vector quantity

From F = BIL sin , the force is a maximum when is is 90i.e. the current andmagnetic field are perpendicular to each other

B sin can be sometimes thought of as being the component of the magnetic fluxdensity which is at right angles ornormal to the conductor


11/19

Estimates of magnetic flux density

The tesla is a large unit of measure

A strong magnet may have a magnetic flux density of a few teslas betweenits poles

The magnetic field strength of an MRI is in the region of 7 teslas

The magnetic field strength due to the Earth in the UK is about 44 T at anangle of 66 to the horizontal


12/19

Exercise

The horizontal component of the Earths magnetic flux density is 1.8 x 10-5T. the current in a horizontal cable is 150 A. Calculate for this cable

a) the max force per unit length

b) the min force per unit length

In each case state the angle between the cable and the magnetic field

Ans:

a) 2.7 x 10-3 N m-1, 90

b) 0, 0


13/19

13

Force Between Two Conductors

Parallel conductors carrying

currents in the same

direction attract each other

Parallel conductors carrying

currents in the oppositedirections repel each other


14/19

Force between parallel conductors

Since a current carrying conductor has a magnetic field around it, if a secondcurrent carrying conductor is place near and parallel to the first, this secondconductor will be in the magnetic field of the first and hence by the motoreffect will experience a force

By a similar reasoning, the first conductor will also experience a force

By Newtons III law, these forces will be equal and opposite

Experiment shows that if the currents are in the same direction. The 2 wiresmove towards each other, and if they are in opposite directions they moveapart from each other

Can confirm using Flemings LH rule


15/19

15

Uses of the turning effect of the force

A moving coil meter

Consists of a rectangular copper coil with many turns of wires inthe magnetic field of a permanent magnet

Can be used to measure current, voltages etc

when a current I is passed through a rectangular conducting coil ofN turnssuspended in a strong magnetic field B, a torque T acts on the coil giving the coil a

deflection through an angle . the torque is balanced by an opposing spring torque ofc where c is the spring's

elastic characteristics.

T = BANI = c where A is the cross sectional area of the coil.


16/19

16

The moving-coil loudspeaker

are widely used in radio receivers, televisions or public addresssystems that apply the principle of a current-carrying conductorplaced in a magnetic field.

When an alternating current of the same frequency as the soundflows continuously in the speed coil, a mechanical force acts onthe coil.

So the coil vibrates along its axis at a frequency equal to theaudio-frequency alternating current flowing through it. The coiland cone vibrate at the same frequency and produce oscillations

in the large mass of air in contact with the cone.


17/19

17

A direct current motor

Consists of a rectangular coil which is free to move in a U-shaped permanent magnet

Together with a commutator and carbon brushes powered by a

power supply Has a catapult effect


18/19

18

Defining Ampere and Coulomb

The force between parallel conductors can be used to define theAmpere (A)

If two long, parallel wires 1 m apart carry the same current, and themagnitude of the magnetic force per unit length is 2 x 10-7 N/m, thenthe current is defined to be 1 A

The SI unit of charge, the Coulomb (C), can be defined in terms of the

Ampere (A) If a conductor carries a steady current of 1 A, then the quantity of

charge that flows through any cross section in 1 second is 1 C


19/19

19

Comparing and summarising the effects

of fields

There are close analogies between gravitational and electric fields but in some

ways they behave very differently

Because masses always attract each other, a mass placed in a gravitationalfield will always move in the direction of the field, from a position of higherpotential to a lower potential

Charges on the other hand will move in the direction of the electric field ifpositive (from a position of higher potential to a lower potential just like a mass

in a gravitational field) or against the direction of the field (and from a lowpotential to a high potential) ifnegative

The field strength for both gravitational and electric fields obey an inversesquare law relationship and the potential obeys a reciprocal relationship withdistance from the source of the field

However a stationary charge in a magnetic field is unaffected, whereas amoving charge experiences a force given by F = Bqv sin and the direction ofthe force is given by Flemings LH rule

Finally, a current-carrying conductor in a magnetic field does not experience aforce if the conductor is parallel to the field direction, but for all other directions itexperiences a force given by F = Bqv sin and the direction is again determinedby Flemings LH rule

Documents

Section v 22 Electromagnetism