Download Topic 5.1 Electric Force and Field

Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
© Kari Eloranta
2016
Jyväskylän Lyseon lukio
International Baccalaureate
August 15, 2016
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Charge
Electric Charge Q
Electric charge Q
Electric charge is the physical
property of matter that causes
electromagnetic interaction.
The types of electric charge
are negative and positive.
In any process, electric
charge is not created or
destroyed.
Law of Conservation of Electric
charge
The total electric charge of an
isolated system remains
constant.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Conductors and Insulators
Electric Conductors and Insulators
Metallic materials, such as copper, aluminium, and steel, are examples of
electrical conductors.
Electrical conductivity in metals can be understood in terms of free electrons
in a metallic substance.
Non-metallic materials, such as most plastics, rubber and wood, are electric
insulators.
There are virtually no free electrons in non-metallic materials.
Semiconductors, which are the widely used in modern electronics, have
physical properties of conductors and insulators.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Force
Coulomb’s Law
Static charges experience an electric force.
Charles Coulomb 1785: the electric force between two point charges is
proportional to the product of the charges, and inversely proportional to the
distance squared between them.
Coulomb’s Law
The electric force between two point charges q1 and q2 at vacuum is
1 q1 q2
q1 q2
F=
=k 2
2
4πϵ0 r
r
where ϵ0 = 8.85 × 10−12 C2 N−1 m−2 is the permittivity of free space,
k = 8.99 × 109 Nm2 C−2 is the Coulomb constant, and r is the distance between
the charges.
Electric force may be either repulsive or attractive. Like charges repel and
unlike charges attract each other.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
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Topic 5.1 Electric Force and Field
Electric Force
Coulomb’s Law in Medium
The Coulomb’s Law on the previous page is valid as such in air.
For other media the law has to be modified. For that we introduce a new
quantity, the relative permittivity of the material.
The relative permittivity of the material, ϵr , expresses how much the electric
force between the two interacting charges is reduced in the medium.
Coulomb’s Law
The electric force between two point charges q1 and q2 in a medium is
1 q1 q2
F=
4πϵrϵ0 r 2
(2)
where ϵr is the relative permittivity of the medium, ϵ0 = 8.85 × 10−12 C2 N−1 m−2 is
the permittivity of free space, and r is the distance between the charges.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Field
Electric Field
Electric charge creates an electric field around a charged object.
The simplest type of a charged object is a point charge, which is very small
electrically charged object.
In a field line representation, the density of the lines represents the field
strength, and arrowheads the direction.
3
3
2
2
1
1
+
0
−
0
-1
-1
-2
-2
-3
-3
-3
-2
-1
0
1
2
3
Figure: A positive point charge creates an
outward radial electric field.
© Kari Eloranta 2016
-3
-2
-1
0
1
2
3
4
5
6
7
8
Figure: A negative point charge creates an
inward radial electric field.
Topic 5.1 Electric Force and Field
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10
Topic 5.1 Electric Force and Field
Electric Field
#»
Electric Field Strength E
When we place a small positive test charge q to a point in an electric field,
the field exerts an electric force on the charge in the direction of the field.
The electric field strength is a quantity that gives the magnitude and direction
of the electric field at a certain point in the field.
Electric Field Strength
The electric field strength is the electric force per small positive unit charge.
Electric Field Strength
The electric field strength is
#»
#»
#»
F
E=
q
where F is the electric force on a small positive test charge q at a point in the
electric field.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
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Topic 5.1 Electric Force and Field
Electric Field
#»
Electric Field Strength E (cont.)
The SI derived unit of the electric field strength is NC−1 (newton per
coulomb)(or V m−1 (volt per metre) as we study later).
Electric field strength is a vector quantity.
Direction of Electric Field
The direction of the electric field at a point is the direction of the electric force on
a small positive test charge at that point.
Charge q should be as small as possible, so that it exerts essentially no force
on the charges which created the field. That way the test charge does not
change the original charge distribution that created the field.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Field
Electric Field Strength of Point Charge
Electric Field Strength of Point Charge
The magnitude of the electric field strength at a distance r from a point charge q
is
q qt
F k r2
q
E= =
=k 2
qt
qt
r
(4)
where k = 8.99 × 109 Nm2 C−2 is the Coulomb constant, and qt a small positive
test charge.
A point charge creates a conservative radial field around itself.
In principle, the field extends to infinity, but decreases rapidly as distance to
the charge increases.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Field
Electric Potential Difference
An electric field is a conservative field: the work done by the electric field on
the charge, as the charge moves from point A to point B in the field, depends
only on the points A and B, not on the path along which the charge travelled.
As the result, we can attach electric potential to all points in an electric field.
Only differences in electric potential have physical meaning, not the value of a
potential on a point which may be artificially normalised.
Electric Potential Difference V
When charge q travels from point A to point B in an electric field, the electric
potential difference between the points is
W
V=
q
where W is the work done by the electric field on the charge.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
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Topic 5.1 Electric Force and Field
Electric Field
Electric Potential
Electric potential is a scalar quantity.
The unit of electric potential is [E ]/[Q] = JC−1 = 1V (joule/coulomb=volt),
according to italian physicist Alessandro Volta (1745 – 1827).
An alternative unit for electric potential is the electronvolt:
1eV = 1.60 × 10−19 J
(6)
which equals the kinetic energy of an electron when the electron is accelerated
by an electric potential difference of 1 V.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Battery and Electric Potential Difference
Electric Potential Difference Across Battery Terminals
A battery is an electrical device that converts chemical energy into electric
energy.
A battery has two metallic connectors called terminals.
There is an electric potential difference between the terminals.
The terminals are called positive and negative based on their electrical
properties.
The positive (+) terminal is at higher electric potential with respect to the
negative (−) terminal.
For example, in a 9 V battery, the electric potential difference across the
unplugged terminals is 9 V.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Battery and Electric Potential Difference
Electric Potential Difference V and Electric Current I
When the terminals of a battery are connected to an electric circuit, an
electric field is established in the wires, and other circuit elements of the
circuit (resistors, lamps, ...).
The field exerts an electric force on the free electrons, while the interactions
between the electrons and the metallic lattice oppose to motion. As a result, a
slow steady electric current flows in the wire.
The free electrons move slowly towards the positive terminal, while electrons
move from the negative terminal into the circuit. The electric current flows
through the battery and the circuit, because the battery sustains an electric
potential difference across the terminals.
A battery produces a direct current (DC) in the circuit. An alternating voltage
source, such as a wall outlet, produces an alternating electric current (AC).
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Current
Electric Current I
Electric Current I
Electric current is the time rate of change of electric charge flowing through a
cross-sectional area in a conductor.
Electric Current I
For a steady direct current, the electric current is defined as
∆q
I=
∆t
(7)
where ∆q is the electric charge that flows trough a cross-sectional area in a
conductor in time ∆t .
The unit of electric current in SI system is
[q] C
= = Cs−1 = 1A (ampere).
(8)
[I ] =
[t ] s
By definition, the direction of electric current is from the higher potential to
the lower potential (the direction of movement of a positive charge in an
electric field).
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Current
Drift Speed
There is a vast number of free electrons in a metal. For example, copper has
about 8 × 1022 free electrons per cubic centimetre.
As a potential difference is applied across a wire, an electric field is established
in the wire. The free electrons start moving slowly against the field from the
lower potential towards the higher potential.
The speed of the free electrons due to electric field is called the drift speed.
Next we derive an equation for the electric current I as the function of the
drift speed v . Suppose that there are n charge carries (electrons) per unit
volume in a wire of cross-sectional area A . Then, in time ∆t , the total charge
∆Q flowing through a cross-sectional area is ∆Q = nV q = n Av∆t q . The
electric current in the wire is thus
∆Q n Av∆t q
I=
=
= n Av q.
∆t
∆t
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
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Topic 5.1 Electric Force and Field
Electric Current
Electric Current I as a Function of Drift Speed v
Electric Current I as a Function of Drift Speed v
If the drift speed of the charge carries (charge q ) is v , the electric current I
flowing through a cross-sectional area A of a wire is
I = n Av q
(10)
where n is the number of charge carries per unit volume (charge density) in the
wire.
Thermal speed of electrons is tens of thousands of metres per second.
Electric field disturbances travel by the speed of light.
A typical drift speed is of the order of magnitude of a few fractions of
millimetres per second! That is really slooooooooow.
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Current
Example on Electric current
Example
A student used an ammeter to measure the electric current of 178 mA in a metallic
wire. How many electrons passes through a cross sectional area in the wire each
second?
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field
Topic 5.1 Electric Force and Field
Electric Current
Example on Electric current
Example
A student used an ammeter to measure the electric current of 178 mA in a metallic
wire. How many electrons passes through a cross sectional area in the wire each
second?
Answer. The electric current in the wire is
∆q
I=
∆t
from where it follows that the electric charge going through a cross sectional area
in the wire in time ∆t is
∆q = I ∆t .
Since the charge of an electron is the negative elementary charge
q e = −e = −1.602 × 10−19 C, the number of electrons passing through a cross
sectional area in a wire each second is
∆q I ∆t 178 × 10−3 A × 1s
18
N=
=
=
≈
1
.
11
×
10
.
−
19
|q e | |q e |
1.602 × 10 C
© Kari Eloranta 2016
Topic 5.1 Electric Force and Field