5.1 Electric fields
We are just about to me struck by
lightning – why are we smiling?
Electric Force and Electric field
What should
we already
know?
Electric Force and Electric field
1. There are two types of electric charge
(positive and negative)
Electric Force and Electric field
2. Static charges can be produced by the action
of friction on an insulator
Electric force and electric field
3. Conductors contain many free electrons
inside them (electrons not associated with
one particular atom)
Electric Force and Electric field
4. Charge is conserved. The total charge of
an isolated system cannot change.
I’m
indestructible!
So am I!
Electric Force and Electric field
5. Opposite charges attract, like charges
repel.
Are you sure?
I’m strangely
attracted to
you!
I’m positive.
Electric Force and Electric field
The force
between two
charges was
investigated by
Charles Augustin
Coulomb in 1785
Electric Force and Electric field
Coulomb found that the force between two point
charges is proportional to the product of the two
charges
F α q1 x q 2
and inversely proportional to the square of the
distance (r) between the charges
F α 1/r2
Coulomb’s law
It follows that
F α q1q2
r2
or
F = kq1q2
r2
Coulomb’s law
F = kq1q2
r2
The constant k is called the Coulomb
constant and has a value of 8.99 x 109
N.m2.C-2
This is valid when the charges are in a
vacuum (or air)
Coulomb’s law
F = kq1q2
r2
The constant k is sometimes written as
k = 1/4πεo
where εo is called the permittivity of free
space. This will change in other
substances e.g. in water etc.
Calculations using Coulomb’s law
The force between two charges is 20.0 N.
If one charge is doubled, the other charge
tripled, and the distance between them is
halved, what is the resultant force between
them?
F = 20N
q2
q1
r
2q1
F=?N
3q2
r/2
Calculations using Coulomb’s law
F = kq1q2/r2 = 20.0N
x = k2q13q2/(r/2)2 = 6kq1q2/(r2/4) = 24kq1q2/r2
x = 24F = 24 x 20.0 = 480 N
F = 20.0N
q2
q1
r
2q1
x = 480 N
3q2
r/2
Electric field
An area or region where a charge feels a
force is called an electric field.
The electric field strength at any point in
space is defined as the force per unit
charge (on a small positive test charge) at
that point.
E = F/q (in N.C-1)
Force on a charge
• This means the force on a charge q is
given by
• F = Eq
• If the charge is a proton or electron
• F = Ee where e = 1.6 x 10-19 C
Electric field around a point charge
If we have two charges q1 and q2 distance
r apart
F = kq1q2
/r2
q1
q2
Looking at the force on q1 due to q2, F = Eq1
Field at q1 = F/Q = kq1q2/r2 ÷ q1 = kq2/r2
E = kq/r2
NOT in data
book
Electric field
Electric field is a vector, and any
calculations regarding fields (especially
involving adding the fields from more than
one charge) must use vector addition.
Field here due to both
charges?
q1
q2
Electric field
Electric field is a vector, and any
calculations regarding fields (especially
involving adding the fields from more than
one charge) must use vector addition.
Field due to q1
Field here due to both
charges?
q1
q2
Electric field
Electric field is a vector, and any
calculations regarding fields (especially
involving adding the fields from more than
one charge) must use vector addition.
Field due to q1
Field due to q2
q1
Field here due to both
charges?
q2
Electric field
Electric field is a vector, and any
calculations regarding fields (especially
involving adding the fields from more than
one charge) must use vector addition.
Field due to q1
Field due to q2
Resultant field
q1
q2
Electric field patterns
An electric field can be represented by
lines and arrows on a diagram , in a
similar ways to magnetic field lines.
The arrows
show the
direction of force
that would be
felt by a positive
charge in the
field
Electric field patterns
An electric field can be represented by
lines and arrows on a diagram , in a
similar ways to magnetic field lines.
The arrows
show the
direction of force
that would be
felt by a positive
charge in the
field
Electric field patterns
An electric field can be represented by
lines and arrows on a diagram , in a
similar ways to magnetic field lines.
This is an
example of a
radial field
The closer the
lines are
together, the
stronger the
force felt.
Field around a charged metal
sphere
E = 0 inside
the sphere
Field around two point charges
Field around two point charges
Field between charged parallel plates
NOT in data
book
d
“Edge effects”
Uniform field E = V/d
V
Parallel plates
• E = V/d and E = F/q
• So V/d = F/q
• Useful!!!!
Remember!
The force F on a charge q in a field E is
F = Eq
Electric field hockey!
•
http://phet.colorado.edu/sims/electric-hockey/electric-hockey_en.jnlp
5.1 Coulomb force and electric
field questions
Electrical Potential (“Voltage”)
The Electrical potential at a point is the
work done per unit charge on a small
positive test charge moving from infinity to
that point. It is given by
Scalar quantity
V=W
q
Note the difference between electrical potential energy (J) and Electrical
potential (J.C-1 – called a VOLT)
Moving charges in potentials
If a charge q is moved from a position with
potential (“voltage”) V1 to a position with
potential V2, work = q(V2 – V1) = qΔV =
ΔEp
V2
(independent of path)
V1
ΔV is called the potential difference or p.d.
Work done accelerating a charge
V = W/q so W = Vq where V = potential
difference
This means when a charge q ia acclerated
by a potential difference (“voltage”) V the
energy gained by the charge is equal to
Vq. An important result to remember!
Electrical potential energy
Electrical potential energy at a point is
defined as the work done to move a
positive charge from infinity to that point.
Uel = kQq
r
Equipotential surfaces/lines
Ep = -GMm
r
Equipotential surfaces/lines
Field and equipotentials
• Equipotentials are always perpendicular to field lines.
Diagrams of equipotential lines give us information about
the gravitational field in much the same way as contour
maps give us information about geographical heights.
Field strength = potential gradient
In fact it can be shown from calculus that
theElectric field is given by the potential
gradient (the closer the equipotential lines
are together, the stronger the field)
E = dV
dr
Electronvolt
A useful unit of energy in Physics. Defined
as the energy gained when an electron is
acclerated by a potential difference of 1
Volt.
W = Vq = 1V x 1.6 x 10-19C = 1.6 x 10-19 J
1 eV = 1.6 x 10-19 J
Current
When a field is applied in a conductor that
contains free electrons, the electrons “drift”
in the direction of the field. This is called
an electric current.
5.1 Electric vocabulary
Let’s just stop for a moment to think about
where these words come from. It will also
aid our understanding
Electric vocabulary
Conventional current and
electron flow
Electron drift speed
Without an applied electric field, the
electrons are moving randomly at a speed
of about 1570 km.s-1! (known as their
Fermi velocity) but there is no net/resultant
movement of charge.
Electron drift speed
• The drift speed is the average speed that
a particle, such as an electron, attains due
to an electric field. In general, an electron
will 'rattle around' randomly in
a conductor at the Fermi velocity. An
applied electric field will give this random
motion a small net velocity in one
direction.
Drift speed
The drift speed v is given by the following
formula:
I = nAvq
I = current (A)
n = charge carrier density (m-3)
A = cross-sectional area of conductor (m2)
v = drift speed (m.s-1)
q = charge on carrier (C)
Derivation
•
•
•
•
•
•
•
•
‘Current’ means the rate at which electric charge flows past a point in a circuit. Imagine standing
at point X with a stopwatch and timing the charge flowing past. (We have to imagine that all the
electrons move at the same speed, v.) We'll watch what happens to the electron highlighted in
red.
Suppose you start your watch and let it run for a time, t. The highlighted electron electron will have
travelled a distance l. In fact, in time t, all of the electrons in the cylinder of
length l haveflowed past you.
So what current has flowed? We need to work out how much charge has passed point A.
Volume of cylinder = A × l where A is the cross-sectional area of the wire. If concentration of
electrons in the metal is n per cubic metre then:Number of electrons in cylinder = n A l
If each electron carries charge Q then:Charge carried by electrons in cylinder = nAlQ
But the length of the cylinder is v * t where v is the drift velocity and t is the time we
used
So:Charge carried by electrons in cylinder = n × A × v × t × Q
This is the amount of charge which passes point A in time t. To find the current which this
represents, we need to find the rate at which the charge has flowed. So we divide by the time t.
Current = charge / time = n × A × v × t × Q / t = n A v Q
Example
A current of 3 A flows through a copper
wire of diameter 0.001m which has 8.5 x
1028 free electrons per m3. What is the drift
velocity?
v = I/(nAq)
= 3/(8.5 x 1028x3.14x0.00052x1.6x10-19)
= 2.8 x 10-4 m.s-1 (0.28 mm.s-1)
Compare this with the Fermi velocity!
5.1 Electron drift questions