Download Electromagnetism

AL Physics / Electromagnetism
P.1
Electromagnetism
I.
Magnetic Field
A.
Sketching of magnetic field lines
B.
1.
Sprinkle iron filings onto a transparent plastic sheet placed in a field, e.g. over a natural magnet.
2.
Using small compass to trace out the path of a North pole when it is placed in the field.
Typical magnetic field
II. Magnetic effect of current
Thumb : direction of current
Fingers : direction of magnetic field
Fingers : direction of current
Thumb : direction of magnetic field
AL Physics / Electromagnetism
P.2
III. Force on current-carrying conductor
Current balance.
F  BIl sin 
F in N, B in T, I in A, l in m.  : angle between I and B
IV. Forces on a moving charge in a magnetic field
F  BQvsin 
F in N, B in T, v in m s-1, Q in C.  : angle between I and B
AL Physics / Electromagnetism
P.3
FB  BQv
I
BI
FB  BQ

nQA nA
QV
FE  QE 
d
FE  FB
QV H
BI

d
nA
BId
VH 
nQA
BI
VH 
nQt

For negative charge carriers, e.g. metal, the block will have a higher potential at the lower surface.

For positive charge carriers, e.g. some semiconductor, the block will have a higher potential at the upper
surface.

The hall voltage is more apparent in semiconductor that in conductor.

Uses:
1.
Finding out the sign of charge carriers.
2.
Finding out the charge density of a conductor.
3.
Measuring magnetic field strength. (Hall probe make use of the Hall effect to measure steady magnetic
field.)
VI. Measurement of magnetic field
A.
Hall probe

Hall probe is used to measure steady magnetic field ( which do not changes with time ).

Hall probe consists of a small piece of semiconductor with a small current passing through it.

It is connected to a high resistance voltmeter through a circuit box.
AL Physics / Electromagnetism

P.4
When the battery in the circuit box is switched on, the ‘balance’ control is adjusted for zero deflection on the
voltmeter.

Then the probe can be inserted into the field to be measured.

The plane of the specimen should be rotated until the voltmeter shows the greatest reading to make sure that
the current is perpendicular to the magnetic field.

Then by measuring the magnitude of the Hall voltage, the magnetic field strength can be found by
B

B.
nQt
VH
I
Note that the Hall probe must be calibrated in Tesla by a known magnetic field before using it.
Current balance
B
C.
F
Il
Search coil

Search coil is used to measured varying magnetic field, e.g. magnetic field produced by alternating current.

A typical search coil has 5000 turns of wire and an external diameter less than 1.5 cm so that it samples the
field over a small area.
AL Physics / Electromagnetism

VII.
A.
P.5
Its two terminals is connected to the Y-plates of a CRO with the time-base off.
Magnetic field around current carrying conductor
Magnetic field around a long straight wire
B

B.
o I
2r
o is called the permeability of free space which has a value of 4  10-7 T m A-1
Magnetic field inside a long solenoid
B
 o NI
  o nI
l
where n is the no. of turns per unit length.

The above expression only hold for very long solenoid whose total length is at least ten times its
diameter.
2)
Direction

3)
The direction of magnetic field inside solenoid can be determined by the Right hand grip rule.
Experiment on finding the magnetic field strength along a solenoid
AL Physics / Electromagnetism
C.
Definition of
1)
P.6
Ampere
Forces between long parallel wires

Two long straight wire, carrying current and parallel to each other, can exert a force on each other.

Then the force experience by wire X due to this magnetic field is
Fx  BY I X L X 

Similarly, the force experience by wire Y due to the magnetic field produced by X is
FY  B X I Y LY 
3)
 o IY I X
Lx
2d
 o I X IY
LY
2d
Definition of Ampere
Currents has unit of ampere which is defined in terms of the force between
currents in long straight parallel conductors. When currents flow in each
of two infinitely-long parallel straight wires of negligible cross-sectional
area, separated by a distance of 1 meter in vacuum, produces a force of
magnitude 2  10 -7 N m-1 between the wires is said to be of 1 A.
AL Physics / Electromagnetism
VIII.
P.7
Torque on a rectangular coil
  NBAI
  NBAI sin 
IX. Moving coil galvanometer
A.
Structure
B.
Theory
  BIAN
opp  c
BIAN  c
C.
Sensitivity

I



NBA
cR
Sensitivities are usually expressed in mm per A or mm per V.
X. Direction of Induced E.m.f
A.
NBA
c
Voltage sensitivity is defined as the deflection per unit p.d. across it.
V


Revision
1.
Fleming's right hand rule
AL Physics / Electromagnetism
2.
P.8
Lenz's Law
The induced current flows always in such a direction as to
oppose the change causing it.

In (ii), when the N-pole is moving towards the coil, to oppose this motion, the end X should be North
pole. By the right hand grip rule, the current should flow in the colckwise direction as view by the
observer.

In (iii), when the coil is moving away from the N-pole, by Lenz's Law, the end X of the coil should be
South pole. By the right hand grip rule, the current should flow in the anti-clockwisedirection as viewed
by the observer.
Q16:
Try to use Lenz's Law, Fleming’s left hand rule and conservation of energy to find out the direction of
induced current instead of using Fleming's right hand rule?

Note that induced e.m.f. will be produced whenever there is a moving conductor in a stationary magnetic
field or a stationary conductor in a changing magnetic field. However induced current will only be
produced when the circuit is complete.
.
AL Physics / Electromagnetism
P.9
XI. Magnitude of Induced E.m.f.
A.
Definition of magnetic flux
The magnetic flux through a small plane surface is the produce of the
flux density B normal to the surface and the area of the surface A.
  BA
  BAcos 

S.I. unit : weber (Wb) which is equivalent to T m2
B in T, A in m2,  angle between B and the normal of A
B.
Faraday's Law of electromagnetic induction

It states that
The induced e.m.f. is directly proportional to the rate of change of magnetic
flux linking the circuit or coil.


d
dt
The negative sign shows that the induced e.m.f. is set up such that it opposes the changes causing it.
XII. Moving conductor in stationary magnetic field
A.
Straight conductor
  (BA)
  BA  Bxl
d

dt
AL Physics / Electromagnetism
P.10

 Bxl

t
t
  Bvl
  Bvl sin 
B.
Rectangular coil
  NBAcos   NBAcos t
d
d
d

   NBA cos t    NBA cos t
dt
dt
dt
  NBAsin t
 o  NBA 
XIII.
A.
Generator
Simple a.c. generator
AL Physics / Electromagnetism
B.
D.c. generator
XIV.
A.
D.c. motor and back e.m.f.
D.c. motor
P.11
AL Physics / Electromagnetism
B.
P.12
Back e.m.f.

Once the coil starts to rotate, e.m.f. is induced in the coil due to the relative motion between the coil and the
magnetic field.

Variation of Current
Ic 
V
:
e.m.f. of the power supply

Rc
:
:
back e.m.f.
coil resistance
V 
Rc
VI c  I c2 Rc  I c
VI c is the power supplied by the power supply.
I c2 Rc is the power dissipated in the coil resistance as heat.
I c is the power loss due to the induced e.m.f. which is in fact the mechanical power developed in the motor.

A motor driving a load takes a greater final steady current than an unloaded one since a greater torque is
required.
XV. Search coil --- Induced e.m.f. in a stationary conductor in a changing magnetic field
  NBA
d
dB

  NA
dt
dt
B  Bo cost
AL Physics / Electromagnetism
P.13
  NBo A sin t
XVI.
A.
Eddy current
Theory
(a) stop quickly

(b) vibrate a few time before stopping
The laminations should be at right angles to the induced e.m.f., i.e. along the plane of motion and magnetic
field, then the eddy current is greatly reduced. And this will not affect the magnetisation of the core as it acts
along the laminations.
B.
Practical uses
(1) Induction heating
(2) Damping of Moving-coil galvanometer
AL Physics / Electromagnetism

P.14
To bring the pointer more rapidly to rest, the damping effect must be increased. This can be done by
winding the coil on a metal frame.
(3) Induction cooking
(4) Magnetic levitation
XVII.
Transformer

It consists of two coils, primary and secondary coil, winding on an iron core with laminations as shown.

It can be used to step-up or step-down the voltage of an a.c. supply.

When an a.c. supply is connected across the primary coil, an alternating magnetic field is set up in the iron core.

If the magnetic field strength in the iron core is B, the area of the plane of coils is A and the number of turns of the
primary and secondary coils are NP and NS respectively. Then the magnetic flux through the plane of the primary
coil and secondary coil are
AL Physics / Electromagnetism
P.15
 P  N P BA
 S  N S BA
dB
P  NP A
dt
dB
S  NS A
dt
VP N P

VS
NS
V P I P    VS I s

Circuit symbol:

To improve the efficiency of the transformer, we can
1.
use thinner wire to reduce the current.
2.
use laminated core to reduce eddy current..
3.
use soft iron core which can be magnetized easily.
4.
improve the design to reduce the magnetic flux leakage.
XVIII. Self-induction

Consider a coil connect to an a.c. power supply,
AL Physics / Electromagnetism
A.
P.16
Effect on current
 back   L
dI
dt
There is a negative sign since the induced e.m.f. opposes the change of current.

S.I. unit of L is henry, H which is equivalent to V s A-1.

That means when back is in volt (V) and dI/dt is in ampere per second (A s -1), the self-inductance L will be in
henry (H).
C.
Energy stored in inductor

Energy
=
W.D. against induced e.m.f.
=
 VI dt
=
  L dt  I dt
=
 dI 


L  I dI
Energy stored in inductor 
D.
LR series circuit
V    L
1 2
LI
2
dI
dt
AL Physics / Electromagnetism
E..
P.17
Implication for switch design

When the switch is open, the current drop from a steady value to zero within a very short time. As a result, the
back e.m.f. built up is very large which may result in dangerous sparks and breakdown of the circuits.

To prevent the building up of a large back e.m.f., a capacitor may be connected in parallel with the switch.

The capacitor allow the current decay slowly instead of dropping to zero immediately. So there is no large
back e.m.f. built up in the coil and prevent accident occur.
END