Charges, voltage and current
Lecture 2
1
Atoms and electrons
-
• Atoms are built up from
– Positively charged nucleus
– Negatively charged electrons
orbiting in shells (or more
accurately clouds or orbitals)
+
-
Negative charge = positive charge
so atoms are
NEUTRAL
Lecture 2
2
1
Electric charge
• Electric charge is measured in Coulombs
(symbol C)
The charge on the electron is - 1.6021892 x 10-19 C
The charge on the proton is +1.6021892 x 10-19 C
usually referred to as e
This is a fundamental constant of our universe
The symbol that we use
for charge in equations is
usually
Q or q
Charles Augustin de
Coulomb
(1736 – 1806)
Published the inverse
square law of electrical
attraction
Lecture 2
3
Free charges
We can remove electrons from (some) atoms quite easily
Heating
The positively charged
Electrical sparks
atom left behind is called
Friction
an ion
Photo-electric effect
Separated electric charges have a very strong force between
them (the electrostatic force)
+
+
Like charges repel
+
Opposite charges attract
The force obeys the inverse square law
Lecture 2
4
2
Inverse square law
F
q1
+
-q1 -
q2
+
r
F
F =
F
F
+ +q2
q1 q2
4πε 0 r 2
Units: Newtons when charges are in
coulombs and distance in metres
ε0 (epsilon nought) is called the permittivity of free space and
is another fundamental constant of our universe which relates
electrostatic effects to force (and so to energy)
ε0 = 8.854188 x 10-12 C2 N-1m-2
Lecture 2
5
Inverse square law
F
q1
+
-q1 -
q2
+
r
F
F
F
F =
+ +q2
q1 q2
4πε 0 r 2
The force between two charges of 1 C separated by 1 metre:
F =
1
4πε 0
Newtons
approximately 9,000,000,000 N or 916,000 tonnes!!
The electrostatic force is by far the strongest physical force that
we normally experience and is responsible for all of the
macroscopic properties of matter
Lecture 2
6
3
Electric field
The electrostatic force can be expressed in terms of ELECTRIC
FIELD (symbol E)
A vector field surrounding charges with
magnitude proportional to the force on a point charge
direction in the direction of the force on a positive charge
(i.e. electric field arrows point towards NEGATIVE charges)
F = qE
(units of E for now, N C-1)
Lecture 2
7
Electric field surrounding point
charges
E
+
-
E (r ) =
q
4πε 0 r 2
Lecture 2
8
4
Moving electrons
A free electron in an electrostatic field experiences a force and so
it accelerates and gains kinetic energy.
The further it moves through the field, the more energy it gains.
v
v=0
-
F
E
-
F
d
Lecture 2
9
Moving electrons
v
v=0
E
F
-
F
d
In a uniform field, force is constant, so velocity increases like
v2 =
2 Eqd
m
1 2
mv = Eqd
2
The electron kinetic energy increases linearly with distance
along the electric field
Electronics is all about exploiting energetic electrons
Lecture 2
10
5
Direct application of fast electrons –
the cathode ray tube
Colour TV or monitor tube
A. Electron gun
B. Glass vacuum envelope
C. Beam deflection and focusing
F. Phosphor screen
Carbon nanotubes for a modern Field-Emission Display
Small CRT e.g. for an oscilloscope
Lecture 2
11
Potential differences – THE VOLT
K.E.
0
P.E. P.D.
5J
5V
++++
+ Q=1
1J
C
4J
4V
2J
3J
3V
3J
2J
2V
1J
1V
0
0
4J
E
5J
-----
• A charge in an electric field has
POTENTIAL ENERGY
• As it moves through the field it gains
KINETIC ENERGY
• The increase in K.E. for a charge of 1 C is
called the POTENTIAL DIFFERENCE or
ELECTROMOTIVE FORCE (e.m.f.)
This is such an important parameter that it has its own unit –
the VOLT (derived from J C-1)
Lecture 2
12
6
THE VOLT (symbol V)
• A potential difference of
1 volt will give 1 joule
of kinetic energy to a
charge of 1 coulomb
Energy = QV
Alessandro Volta (1745-1827)
Credited with constructing the
first chemical battery
Lecture 2
13
A demonstration “Voltaic
pile” from ~1825
Two “dry piles”, insulated
with sulphur
-
+
+
-
+
-
The metal ball suspended
on a silk thread alternately
charges + and – and
oscillates between the bells
Claimed to be the “world’s
most durable battery”
(Guinness Book of
Records) or (popularly) a
perpetual motion machine!
Clarendon Laboratory
‘Museum’, Oxford
Lecture 2
14
7
An analogy
P.E. = mgh
who?
K.E.
0
P.E. P.D.
5J
5V
++++
+ Q=1
1J
C
4J
4V
2J
3J
3V
3J
2J
2V
1J
1V
0
0
F=EQ
4J
F=mg
E
5J
-----
K.E. = ½mv2
A charged particle moving in an electric field has exactly the
same dynamics as a mass falling under gravity
Lecture 2
15
A new definition for electric field
We can now define electric field in terms of VOLTAGE
Remember that
Field is Force per unit charge
(newtons per coulomb)
Voltage is energy per unit charge (joules per coulomb)
Energy is Force x Distance
(joules = newton.metres)
so Voltage = Field x distance
Field = Voltage / distance:
+V
l
E=V/l
Units V m-1
In a uniform field, E=-V/l,
In a non-uniform field,
V=-El
E (l ) = −
dV
dl
l
Lecture 2
V = − ∫ E (l )dl
0
16
8
Current
• Moving charged particles transport charge from one point
to another
• The rate of charge transport across any surface is called the
CURRENT [symbol in equations i or I, unit Ampères (A)]
If N particles of charge q
cross a surface in time t, the
current is given by
i=
Nq
Ampères
t
The early experimenters got it wrong. Current is carried by electrons and so
we have to remember that current flow is OPPOSITE to electron flow.
Electrons: Negative to Positive
Current: Positive to Negative
Lecture 2
Statue in Lyon
17
André-Marie Ampère (1775-1836)
Investigated the magnetic effects
of electric currents
Lecture 2
18
9
Current and charge
In practice, the flow of charge carrying particles is not constant
with time so we have to use a differential definition for the
instantaneous current at a particular time t:
dq
i (t ) =
dt
where dq is the small amount of
charge (C) which flows in the small
time from t to t+dt (sec).
To get the total charge that has flowed
in a particular time period we need to
integrate the current:
t2
Q = ∫ i (t )dt
t1
If current is constant, charge=current x time
current = charge/time
Lecture 2
19
Current flow and power
Moving electrons carry ENERGY as well as charge, and so an
electric current has POWER (rate of arrival of energy)
[symbol in equations P, unit Watt = 1 Joule per second, W]
Similarly to current we can define the power as
P(t ) =
dE
dt
where dE is the small amount of energy
crossing our surface between t and t+dt
We already know that the energy of a particle of charge q
coulombs with voltage V volts is qV joules, so
P(t ) = Vi (t )
Lecture 2
watts = volts x amps
20
10
James Watt (1736-1819)
Scottish engineer most famous
for the development of steam
power – he was the first to use
the term ‘horse-power’
Lecture 2
21
Active and passive components
+V
+V
I
I
W
Passive:
• Current flow is in the direction
of the voltage (+ to -)
• Power is absorbed from the
current by the components and
transferred to the surroundings
W
Active:
• Current flow is in the OPPOSITE
direction to the voltage (- to +)
• Power is absorbed from the
surrounding by the components and
transferred to the current flow
Lecture 2
22
11