ELECTRICITY & MAGNETISM
CHAPTER 8
E & M - Focus
Electric Charge &
Force
Magnetism
Current, Voltage
& Power
Electromagnetism
Simple Electrical
Circuits
Voltage & Current
Transformation
Electric Charge & Force
Gravitational Case
Electrical Case
m1m2
Fg = G 2
r
q1q2
Fe = k 2
r
s
e
rg
e
k
i
nl
-
a
h
C
+
U
s
e
rg
+
+
Only One Kind of Mass
e
k
i
L
a
h
C
Electric Current, I
Vehicle “current”
Electric current
kg (mass of vehicles)
current =
time
charge
current =
time
q
I=
t
coulombs
amperes =
second
Electric Potential Energy - V
Gravitational Case
Electrical Case
Fg is assumed to be constant
Fe is not constant
m
PEg = wh = mgh
w
h
q1
W
V=
q
joules
volts =
coulomb
Fe
d
Fe
q2
Batteries - Sources of Voltage
+
1.5V
-
q
Move charge q from one battery pole to another. How much work did you do?
W = Vq
Note that is does not matter what path the charge goes through!
Electrical Resistance - R
• Conductors support high
electric currents because
of mobile electrons.
• Semiconductors have few
mobile electrons.
• Insulators have no mobile
electrons.
• Conductors have low (but not zero) resistance.
• Semiconductors have high
resistance.
• Insulators have infinite resistance.
Resistance - Gravity Case
These guys are doing
work against gravity,
but their also doing work against friction.
h
Electrical Resistance - R
Circuit Elements
Electrical Resistance - R
V
R=
I
V
R=
I
V
I=
R
V = IR
volts
ohms =
amp
The vulture is above the iguana.
The vulture is above the rabbit.
The iguana and the rabbit are on the same level.
Electrical Power - P
Work
Power =
Time
W
P=
t
joules
watts =
second
Recall the equations for I and V
q
I=
,
t
W
V=
q
…and so, rearranging things
qW W
IV =
=
=P
t q
t
P = IV
Electrical Power - P
From
And
We get
P = IV
P = IV
V = IR
V
=I
R
P=I R
2
2
V
P=
R
Simple Electrical Circuits
Series
Parallel
But First - Gravity!
Series
water
h
wheels
h1
h2
h3
Key Points:
• The flow of water through each wheel is the same.
• The total potential energy drop
∝h=h
1
+ h2 + h3
But First - Gravity
Cw
C1
C2
C3
C1
C2
C3
Parallel
water
h
wheels
Key Points:
• Water flow is split unevenly over 3 wheels. Cw = C1 + C2 + C3
• The total potential energy drop, h is the same for each wheel.
Series Electrical Circuit
We know
V = IR
and
so,
V1 = IR1
V1 + V2 + V3 = V = IR1 + IR2 + IR3
V2 = IR2
V3 = IR3
Equivalent series resistance:
V = I ( R1 + R2 + R3 )
Req = R1 + R2 + R3 + ...
Parallel Electrical Circuit
We know
V
I=
R
and
V
I1 =
R1
V
I2 =
R2
V
I3 =
R3
so,
V V V
I1 + I 2 + I 3 = I = +
+
R1 R2 R3
⎛ 1
1
1⎞
I =V⎜ +
+ ⎟
⎝ R1 R2 R3 ⎠
Equivalent parallel
resistance:
1
1
1
1
= +
+ + ...
Req R1 R2 R3
Batteries in Series
+
1.5V
-
+
1.5V
-
+
1.5V
Total = 4.5 V
Batteries in series can supply 3 times the voltage at the same current.
-
Batteries In Parallel
Batteries in parallel can supply
3 times the current at the same
voltage.
+
1.5V
-
+
1.5V
-
+
1.5V
-
Total = 1.5 V
Magnetite, or Loadstone
MAGNETISM
Early Magnetite
Compass
Gravity, Electric Analogies
Gravity
• Only one kind of
mass
• Attractive only
Electricity
• Two kinds of
charge, + and -
• Opposites attract,
Like charges repel.
Magnetism
• There are no
magnetic charges,
only fields!
• Opposite poles
attract, Like poles
repel.
Background - Earth Magnetism
• Geomagnetism:
Magnetite Compass
was used for navigation.
• Paleomagnetism:
Most rocks have residual
magnetism from the time
of their solidification.
The Magnetic Field
Thought Experiments:
• Tiny “test”
compasses could be
used to “map” a
magnetic field.
Also:
• You could do this
with a test mass to
map a gravitational
field.
• You could do this
with a test charge to
map out and electric
field.
Electric Current & Magnetic Field
Moving charge creates a
magnetic field.
I
R (wire)
+
-
V
Magnetic
Field
A flow of electric current
comes with a magnetic
field.
Electric Current & Magnetic Field
In a loop, the magnetic
field becomes more
concentrated at the center.
I
R (wire)
+
-
V
Magnetic
Field
Electric Current & Magnetic Field
In a coil, the magnetic field
becomes even more
concentrated at the center.
I
+
-
S
V
R (wire)
N
Magnetic
Field
Right Hand Rule for I
If your right thumb points
in the direction of
conventional current, then
your fingers point in the
direction of the magnetic
field (B-field).
Magnetic Force On Moving Charges
• Relative motion
between the
magnetic field and
the charge is what
counts.
• For negative charges
(electrons) use you
left hand.
• If a conductor is
passed though a
magnetic field, a
current can flow!
Electrical Generation
Changing Magnetic Field
A changing magnetic field can also
induce electric currents.
Output from
AC generator
on previous
slide
I
I
R, load
Alternating
Magnetic
Field
This induced current
can drive a useful
electrical device.
The Transformer
Transformers are used to
change voltage and
current levels in practical
power distribution
networks.
⎛ N2 ⎞
V2 = ⎜ ⎟ V1
⎝ N1 ⎠
⎛ N1 ⎞
I 2 = ⎜ ⎟ V1
⎝ N2 ⎠
Note: Power is conserved
⎛ N1 ⎞ ⎛ N 2 ⎞
P2 = I 2V2 = ⎜ ⎟ I1 ⎜ ⎟ V2 = I1V1
⎝ N 2 ⎠ ⎝ N1 ⎠
P2 = P1
V
The Power Grid