Download Magnetic field? - the SASPhysics.com

Electromagnetism
Magnetic Fields
• Magnetic field: a region where
another magnet (or magnetic
material) feels a force
• Field lines show direction of force
on a N pole
• Magnetic field strength aka
Magnetic Flux density, B
– A vector quantity
– unit: Tesla
– Indicated by density of field lines
Reminder: Magnetic field around a wire
carrying current
•Direction of field given by Maxwell’s Right
Hand grip rule (or think of a screw thread).
A reminder of some B fields
Magnetic force on moving charges
– Demo
Motion
• An electrical charge moving in a magnetic
field experiences a force.
• This is true for electrons moving in a wire
in a magnetic field – the motor effect.
“Fleming’s Left
Hand Rule”
Motor Effect Questions
•A wire carries a current horizontally between the
poles of a magnet, as shown below. The direction
of the force on the wire is:
•A from N to S
•B from S to N
•C opposite to the current direction
current
•D In the direction of the current
•E vertically upwards?
N
S
Motor Effect Questions
•In the figure below, AB is a copper wire hanging from
a pivot at A and dipping into mercury in a copper dish
at B. It is suspended between the poles of a powerful
magnet.
•(a) Copy the diagram and add the magnetic field lines
•(b) Mark in the direction of the conventional current
•(c) What will happen when the switch is closed?
A
N
S
B
Force on a current-carrying wire
• Do the Experiment
Force on a current-carrying wire
• Experimentally we find the force is proportional
to:
– The magnetic flux density (B)
– The current flowing in the wire (I)
– The length of wire (l)
• We can write:
F  BIl
(Only true for current and field perpendicular. More
generally: F=BIlsin)
Definition of the Tesla
• 1T is defined as the magnetic flux density
which produces a force of 1N on a 1m
length of wire carrying a current of 1A at
right angles to the field.
• 1T=1 NA-1m-1
Definition of the Ampere
[Not examinable]
• Parallel wires carrying currents
will exert forces on each other.
– Each wire produces a magnetic
field, which influences the other
wire.
• The ampere is defined as the
constant current which, if flowing
in two straight parallel conductors
placed 1 metre apart in a
vacuum, would produce between
these conductors a force equal to
2×10–7 newtons per metre of
length
• Sometimes appears
in exam questions
– Make sure you can
apply Fleming’s left
hand rule for the two
cases:
currents in
opposite
directions repel
one another
currents in the
same direction
attract one
another
• the length of wire in a magnetic field is
0.05 m. When a current of 2.5 A flows, a
force of 0.01 N is shown. What is the
magnetic field strength?
– B = 0.08 T
• TAP 412-4
Couple on a coil
• Force on each side of coil with
n turns: F=BILn
• Pair of forces form a couple
• Torque of couple=Force x
distance between them
w
T  BILnw
• But when coil is not
perpendicular to field, the
effective width is wcosa:
T  BILnw cos a
Lw  A, so
T  BIAn cos a
a
B
Electric motor
DC Motor
AC Motor
Force on a moving charge
• Consider a charge Q moving at a speed v:
Q
I
t
l
v  so l  vt
t
Q
F  BIl  B. .vt
t
Force always 90° to velocity – circular motion
F  BQv
• An electron accelerated to 6.0 × 106 ms–1
is deflected by a magnetic field of strength
0.82 T. What is the force acting on the
electron? Would it be any different for a
proton?
F= –7.9  10–13 N
– The value of the force would be the same but
the direction would be opposite.
The Hall Probe
• Used to measure magnetic
field strength
– Current flows through a
slice of semiconductor
– Force on moving charges
due to magnetic field
deflects charges
– Potential difference
between top and bottom of
slice results
– Hall voltage a B field
strength
• An electron passes through a cathode ray
tube with a velocity of 3.7 × 107 m/s. It
enters a magnetic field of flux density 0.47
mT at a right angle. What is the radius of
curvature of the path in the magnetic field?
– F = Bqv and F = mv2/r so r=mv/Bq
– r=44 cm
• Note that radius of track depends on the
charge/mass ratio of particles
• This is how a mass spectrometer works…
Velocity selector
• Force on ions due to electric field
QV
Felec 
d
• Force on ions due to magnetic field F  BQv
mag
• Only particles with certain velocity so
V
v
forces cancel can pass through
Bd
Mass Spectrometer
• It can be shown that only
particles with velocity
v=E/B pass through the
velocity selector
• R=mv/qB=mE/qB2
• If we know the charge
(ionisation state), we can
find the mass of the
particles from the radius
of their path
• This enables us to
analyse the constituents
of complex materials.
Velocity selector
Application: cyclotron
• A cyclotron is a compact particle
accelerator
Lawrence’s Cyclotron
• Particles are
repeatedly
accelerated when
passing between
“dees”
– Velocity increases
– Radius increases
• Time for an orbit
remains constant
– Constant frequency
drive signal
mv
r m
r
, so t semiorbit 

Bq
v Bq
The first Cyclotron
Accelerated protons to 80keV
Electromagnetic induction
• Any conductor
experiencing a changing
magnetic field (or moving
across a steady magnetic
field) will have a p.d.
induced across it.
• If a closed circuit is made,
a current will flow.
• This is the basis of almost
all electricity generation.
1820 – Ørsted discovers B field of current
1831 – Faraday discovers induction
The right hand rule
• Not to be confused
with the left hand
rule...
Electromagnetic induction
Electromagnetic induction
• The direction of the induced voltage can
be reversed by:
– Reversing the magnet
– Moving the magnet in the opposite direction
Electromagnetic induction
• The size of the induced voltage can be
increased by:
– Moving the magnet faster
– Increasing the number of turns on the coil
– Using a stronger magnet
• Adding a soft iron core
Magnetic Flux
• A useful quantity when considering
electromagnetic induction
Unit: Weber (Wb)
1 Wb = 1T x 1 m2
F  B.A
Flux
area
Flux density
• F=BA if area is at 90° to field (F=BAcos
otherwise)
• (Loosely) total magnetic field experienced
by something of a given area
Faraday’s Law
• Faraday found that for an emf to be
induced, a conductor must cut field lines.
• “The induced emf is equal to the rate at
which the circuit cuts magnetic flux”
F
  N
t
emf (V)
Rate of
change
of flux
Lenz’s Law
Number of turns in
circuit
NF – “flux linkage”
Lenz’s Law
• The direction of the induced emf is always
such that it opposes the change inducing it
– Really just the principle of conservation of
energy
– What would happen if it did not oppose it?
• Denoted by the minus sign in the formula.
• Induction demos, 414-11 (diff tubes?)
• Magnet falling through a coil
Generating electricity
• Consider a conducting rod of length L moving at a steady
speed v perpendicular to a field with a flux density B:
• electrons will experience a force Bev along the rod,
creating a separation of charge
• Electrostatic repulsion opposes this.
Ee  Be v
E  V / L  Bv
  BLv
Induced emf
L
v
Flux density (B)
  BLv
• Note:
– area A swept out in time t = Lvt, so:
BLv t

t
BA F


t
t
Faraday’s Law
“emf=flux swept out per second”
How to increase ?
L
v
Flux density (B)
Calculate...
North
Earth’s
B-field
–
70°
+
Faraday’s disc
• When the disc turns
at frequency f an emf
is induced between its
axle and rim
• Think of a thin strip:
• Flux swept out/s=
=BR2f
• With a load have
braking system
Windmills
• The blade of a wind turbine has a radius
12 m and rotates every 6 seconds. The
turbine’s axis is aligned N-S, so the blade
cuts the horizontal component of the
Earth’s magnetic field, which is 20 mT.
• Calculate the emf induced across the
blade.
• Flux swept out/s=
=BR2f=0.0015V
Flux linkage
• Flux linkage = NF = NBA
– N is number of turns on a coil, A is the area
– This is for a coil perpendicular to the field
• If the coil is parallel to the field, flux linkage = 0
• Emf = rate of change of flux linkage
Generators / dynamos
• To generate a continuous voltage we need
a constantly changing magnetic field.
• This is achieved by rotating a magnet in or
near a coil of wire.
• An ALTERNATING
CURRENT is produced.
Alternating output
Magnet position
Dynamos
More usually...
• AC generator is a coil
rotating in a magnetic field
• AC motor run in reverse...
peak =BANw
Figure 1(a)
coil
magnet
slip rings
brushes
Figure 1(b)
e.m.f
time
a.c
output
Figure 1(c)
AC generation
• Flux linkage through coil: NF  BAN cos
• If the coil is spun with an angular frequency w:
  2ft  wt , so NF  BAN cos(wt )
dNF
 
 BAN w sin( wt )
dt
 0  BANw, so    0 sin( wt )
How would you
design a higher
voltage generator?
Induced emf=0 when coil edges moving parallel to B field
Induced emf is max/min when coil edges cut perpendicularly across B field
Increasing generator output
• This can be done by:
– Using a stronger rotating magnet or
electromagnet
– Rotating the magnet faster
– Using fixed coils with more turns
– Putting an iron core inside the fixed coil
Real generators
Battersea Power Station, 1933
Mutual induction
• Remember electromagnets?
– When a current flows in a coil of
wire a magnetic field is produced
• If an alternating current flows,
then an alternating magnetic
field is produced
• If a second coil of wire
experiences this changing
field, a voltage is induced in it
• Run this simulation and click in
the transformer tab
Transformers
• A transformer consists of
two coil mounted on a
common iron core
• An alternating current
flowing in the primary coil
induces a changing
magnetic field
• The iron core
concentrates the field
through the centre of the
secondary coil
• The alternating magnetic
field induces an
alternating current in the
secondary coil
• This happens even
though there is no direct
electrical connection
between the two coils
Transformer action
• A transformer can change the voltage.
• The size of the voltage induced in the secondary coil
depends on the number of turns in the primary and
secondary coils and also the voltage applied to the
primary coil.
Voltage across secondary coil number of turns on secondary coil

Voltage across primary coil
number of turns on primary coil
Vs N s
or

Vp N p
• If Vs>Vp: step-up
transformer
• If Vs<Vp: stepdown transformer
Transformer example
• A transformer has 100
turns on the primary coil
and 300 turns on the
secondary coil. If 20V AC
is applied to the primary
coil, what will be the
voltage on the secondary
coil?
• A device is connected to
the secondary coil which
draws a current of 2 A.
What is the current
flowing in the primary
coil?
Vs N s

Vp N p
300 Vs
 ,
100 20
so Vs  60 V
I pV p  I sVs
I p  20  2  60
Ip  6A
Transformer efficiency
efficiency 
power delivered by secondary coil I sVs

100
power supplied by primary coil
I pV p
• Transformers can be close to 100%
efficient through the use of:
– Low resistance windings
– A laminated iron core to reduce eddy currents
– Using soft iron to minimise magnetisation
losses
Power in a transformer
Power in  Power out
so I pV p  I sVs
• So if a transformer steps up the voltage,
the current is stepped down.
– You can’t get something for nothing!
• This assumes an ideal transformer, where
no energy is lost to heating
Electricity transmission
• When electricity is transmitted over
power lines, some power is lost due
to the resistance of the cables (as
heat)
• P = IV and V=IR so Power lost = I2R
– So the higher the current, the more
power we lose
• A step-up transformer is used to
convert electrical power to very high
voltage (low current) for transmission
over long distances to minimise this
power loss
• It is converted back to a more useful
level at the other end by a step-down
transformer
Typical power transmission system