Inductance, Magnetoresistance,
and You
Different approaches to magnetic
storage
Capacitance
• The battery provides the work needed to move the
charges around and increase their potential energy
• The ratio of charge stored to potential difference
maintained is the capacitance of the object
V +
-q
V
+q
• q is the charge on one plate
q
C
V
What determines capacitance?
• Capacitance depends solely on the geometry of the
capacitor and the medium between the plates
• Larger plates can collect more charge at the same
potential difference than smaller ones
• For the same charge, the potential difference
between plates will increase with separation
between them
• For an empty, parallel plate capacitor
C=0 A/d
Combining capacitors
• Capacitors in parallel
C p  C1  C2
• Capacitors in series
1
1
1
 
Cs C1 C2
Electrical Storage
• Capacitors are used in RAM:
– A charged capacitor is a 1
– An uncharged capacitor is a 0
• Reading a capacitor discharges it, so you must
continually re-write when reading
• Capacitors lose charge over time (charge will
slowly leak into air or other insulator), so
capacitors are not good for long-term storage
A Learning Summary
• Capacitors store charge, thereby storing electric field
and maintaining a potential difference
• Capacitors can be used to store binary info
• Capacitance is found in many different aspects of
integrated circuits: memory (where it’s desirable),
interconnects (where it slows stuff down), and
transistors (ditto)
Magnetic Fields
• Magnetic fields are created two ways:
– By moving charges (currents)
– Intrinsic property of elementary particles
• In most materials, the intrinsic magnetic fields of
nuclei and electrons each cancel
• In ferromagnetic materials, the intrinsic magnetic
fields of electrons can be aligned and added up
• Magnetic field lines point from “North” to “South”
Storing data magnetically
• The electron spins (intrinsic magnetic fields) in a
ferromagnetic material are aligned to give a net
magnetization
• The smallest region with same alignment is called a
“domain”
• If data is digital and binary, two domains are used to
store a bit of storage
• If data is analog, magnetic field varies continuously
in proportion to the data
Representing data magnetically
• Two domains are used to store a bit of
storage
• Magnetizations in the two domains with the
same direction represents a 0
• Magnetizations in the two domains with
opposite directions represents a 1
• The direction of magnetization changes at
the start of a new bit
Examples of magnetic data
N S N S
S N N S
S N
S N S N
N S S N
Domains
Bits representing 0
Bits representing 1
N S
N S N S S N S N N S N S S N S N N S N S S N S N
A string of 0s
A 1 followed by a string of 0s
Examples of magnetic data
N S N S
N S N S S N S N N S N S S N S N
A string of 0s
S N S N
Bits representing 0
S N N S S N N S S N N S S N N S
S N N S
A string of 1s
N S S N
Bits representing 1
N S S N N S S N N S S N N S S N
Examples of magnetic data
S N N S N SS N N S S N S N N S N S
0
1
0
0
N S S N N S S N N S S N N S
1
1
1
Examples of magnetic data
0
1
0
0
1
1
1
Writing magnetic data
• Ferromagnetic material becomes magnetized in
the presence of a magnetic field
• Currents create magnetic fields
• A loop of current creates a magnetic field passing
through the axis of the loop in a direction given by
the “right-hand rule”
• Outside the loop, the field has the opposite
direction, since it is circling back
Writing magnetic data
• Changing the direction of current in the loop
changes the direction of the magnetic field and so
magnetizes the ferromagnetic material in a
different direction
Reading magnetic data - induction
• Faraday (and Henry) discovered that changing
magnetic fields produce electric fields
• This electric field provides the emf needed to move
charges around a loop of wire (current!)
• They also found that changing the area of the loop
in the electric field induces a current
• Using a larger loop, or a coil of multiple loops,
resulted in a larger current than a smaller loop
Faraday’s Law
• The conclusion:
dF B
  iR  
dt
• FB is the magnetic flux, given by
F B   B  dA  BA cos
• A is the area of the loop with B through it
• second equality holds only in simple cases
Faraday’s Law and you
• A changing magnetic field induces emf in a coil of
wires proportional to
–
–
–
–
The number of turns in the coil
The area of the coil
The angle between the coil’s axis and the field
The rate of change of the field
• Moving a magnetized ferromagnetic material past a
coil of wire will induce a current if the
magnetization changes
• Measuring this current provides info on field
Magnetic Forces
• Charges moving through a magnetic field
experience a force (Fact #10)
• This force is perpendicular to both the magnetic
field and the direction of motion
• If the charge is at rest, it experiences no magnetic
force
• If the charge moves parallel (or antiparallel) to
magnetic field, it experiences no magnetic force
Magnetic Forces
 Mathematically,
FB = qv x B
|FB| = |qv| |B| sin 
(  is angle between v and B)
direction given by right-hand rule
Magnetoresistance
• Electrons moving through a current-carrying wire
are moving charges
• If a magnetic field is present in the wire (not in the
direction of current flow), the conduction electrons
will experience a magnetic force perpendicular to
direction of current
• This force pushes electrons off track, increasing
resistance
Conduction
electrons
Magnetic field pointing
into page (screen)
Current-Carrying Wire
Direction of velocity v
of electrons
Direction of qv of
(negative) electrons
Direction of force on
conduction electrons
Magnetic field pointing
into page (screen)
Current-Carrying Wire
Direction of velocity v
of electrons
Direction of qv of
(negative) electrons
So where’s the application?
• The presence of a magnetic field increases the
resistance of a wire
• If a potential difference is applied to the wire,
current will flow inversely proportional to
resistance (i=V/R)
• A change in magnetic field produces a change in
current which can be measured
• This yields a sensitive indicator of change in
magnetic field
Comparison between
Magnetoresistance and Induction
• Magnetoresistance is a much larger effect than
induction
• Magnetoresistance detects magnetic field, not just
the change in magnetic field, so it is less sensitive
to changes in tape/disk speed and other variables
• Equipment needed to detect magnetoresistance
simpler than coils for inductance
• Magnetoresistance replaced induction several
years ago
What have we learned?
• A piece of ferromagnetic material in a magnetic
field retains the magnetization of the field even
after leaving the field
• Currents create magnetic fields proportional to
current
• Changing the direction of current changes
direction of magnetic field
• Magnetic data is written this way
What else have we learned?
• Magnetic storage uses two domains for each
bit of data: parallel domains represent 0,
antiparallel (opposite) domains represent 1
• The first domain of a new bit will have
magnetization opposite from second domain
of prior bit
• This convention allows errors to be caught
What else have we learned?
• A changing magnetic field induces a current in a
loop of wire:
iR = - A(dB/dt) cos 
• A magnetized material moving past a loop of wire
provides such a changing magnetic field
• If current is induced as bit passes, bit is 1; if no
current induced, bit is 0
More Stuff to remember
• A charge moving through a magnetic field
experiences a force perpendicular to the field and
the direction of motion of the charge
• The magnetic force is proportional to the charge,
the magnitude of the field, the velocity of the
charge, and the sine of the angle between v and B
• The effects of this force on charges in a currentcarrying wire lead to effect of magnetoresistance
Before the next class, . . .
• Start Homework 14 (due March 4)
• Do Activity 12 Evaluation by Midnight
tonight
• Read Preface and Chapter 1 in Turton
• Do Reading Quiz