Lecture 10
Electricity
Electric forces are important
Electricity is central to modern society
Forces between atoms are electric in nature. So materials are the way
they are because of the electric forces of their constituent atoms.
Many fundamental processes in atmospheric science involve electricity.
Northern lights (http://climate.gi.alaska.edu/Curtis/aurora/040901_1)
Lightning (www.nasa.gov)
1
Properties of Electric Charges
Two kinds of charge: positive and negative
Positive charges attract negative charges
Positive charges repel other positive charges
Negative charges repel other negative charges
All matter is a mix of:
positively charged protons
negatively charged electrons
uncharged neutrons
Electric charge comes in discrete lumps:
An electron charge is -e = - 1.60 x 10-19 C
(the unit of charge is “coulombs” or “C”)
A proton charge is +e = + 1.60 x 10-19 C
All charge is a multiple of this basic unit.
2
Types of Materials
All materials in the world can be classified according their
electrical properties:
Conductors: electric charges can move freely in conductors
Insulators: electric charges cannot move freely
Semiconductors: flow of electrons can be controlled
3
Separation of charge in a
conduction by induction
Lets begin by considering a charged insulator coming close to
an uncharged conductor ...
http://en.wikipedia.org/wiki/Electroscope#Gold-leaf_electroscope
Show demo and movie
4
Charging by Induction
Lets begin by considering a charged insulator coming close to
an uncharged conductor ...
+ +++++
Charged rod
--
Overall uncharged
“electrically neutral”
conductor
- -+
++
+ +
5
Charging by Induction
1. Charged insulator induces charge separation in conductor ...
+ +++++
Charged rod
--
- -+
++
+ +
+
Charge transferred
to electrical ground
2. If the positive charged end of conductor is brought in
contact with a large reservoir such as the Earth, this charge is
transferred out of the conductor.
6
Charging by Induction
3. When electrical ground is disconnected and charged rod is
removed there is some excess negative charge on the
conductor.
-
-
-
Overall negatively
charged
conductor
-
-
-
Electrical ground
is disconnected
from conductor
4. This negative charge redistributes.
Chargind by induction does not require contact by the object
inducing the charge.
7
Polarization in Insulators
In insulators, there charges cannot move freely.
However, the average position of the positive charge shifts slightly
with respect to the average position of the negative charge.
Such a separation of charge is called a dipole. The dipoles in an
insulator are all randomly oriented.
A material which contains dipoles is said to be polarizable.
Why?
8
Polarization in Insulators
A material which contains dipoles is said to be polarizable.
+ +++++
Charged rod
Electrical ground
is disconnected
from conductor
In the presence of a positively charged rod, the dipoles orient with
the negative end facing the positive charge.
9
Coulomb's Law
The electric force between two charged
objects is:
Proportional to the charge of each object
Decreases with the separation of the two objects
Decreases as the square of the distance of
separation
F e =k e
where
Charles-Augustin
de Coulomb (1736-1806)
1
k e=
4 0
q1q 2
r
2
0 =8.85×1012 C 2 / N.m 2
and
is a fundamental physical constant.
10
Fundamental Physical Constants
We have seen two so far:
The charge of an electron -e (or proton +e)
where e = 1.60 x 10-19 C
The permittivity of free space ε
0
What is NOT a fundamental physical constant?
11
Coulomb's Law
How to deal with the vector nature of the force:
q1
+
r12
r
q2
+
F12
Draw a unit vector (“r-hat”) along the
line joining the two charges, from
charge 1 to charge 2 (r12 ).
If the two charges have the same sign
(as shown on the left) the force has the
same direction as r12
This force is a repelling (“repulsive”)
force
By Newton's Third Law:
F12= F21
12
Coulomb's Law
How to deal with the vector nature of the force:
q1
-
r12
r
F12 q2
+
Draw a unit vector (“r-hat”) along the
line joining the two charges, from
charge 1 to charge 2 (r 12 ).
If the two charges have opposite sign
(as shown on the left) the forcehas the
r12
opposite direction as
This force is an attractive force
And again, by Newton's Third Law:
F12= F21
13
Recall: The Principle of
Superposition for Standing Waves
If two travelling waves are moving through a medium and
combine at a given point, the resultant position of the element
of the medium is the sum of the position of the individual
waves.
Two pulses, both with positive
displacements.
Two pulses,w one with positive and one
with negative displacement.
14
The Principle of Superposition for
Electric Forces
The resultant force on any one particle is the vector sum of the
individual forces on it due to all the other particles.
+
The resultant force on charge 2:
r32
r13
q1 +
q3
r12
r
F2 = F12 F32
q2
+
F32
F12
F12
F2
F32
15
Exercises
Example 19.1: Where is the resultant force zero?
Three charged particles lie along the x axis as in the figure.
+
-
+
q2
q3
q1
2.0 - x
x
q1 =15 C
q 2=6 C
L=2.0 m
2.0 m
Where on the axis can a negative charge q3 be placed such that the
resultant force on it is zero?
16
Example 19.1
1. First draw the unit vectors from 1 to 3 and from 2 to 3.
2. Since q3 and q1 are of opposite sign; and since q3 and q2 are of opposite
sign, the forces point in the direction opposite the unit vectors
r23
F23
+
q2
F13
-
r13
+
q3
q1
L-x
x
q1 =15 C
q 2=6 C
L=2.0 m
L = 2.0 m
q1 q 3
q 1 q3 i
F13 =k e
r =k e
2 13
2
L x L x F23 =k e
q 2 q3
x2
i
is the unit vector along
the positive x direction
q2 q3 r23 = k e 2 i
x
17
Example 19.1
Set the sum of forces on charge q3 to zero and solve for x.
F 3 =F13 F23= k e q 3
q2
x
2
q1
2
Lx =0
q1 =15 C
q 2=6 C
L=2.0 m
Notice that q3 is common to both the terms and comes out of the brackets.
So it turns out the condition for zero force does not depend at all on q3.
Solving the equation:
18
Example 19.1
Set the sum of forces on charge q3 to zero and solve for x.
F 3 =F13 F23= k e q 3
q2
x
2
q1
2
Lx =0
q1 =15 C
q 2=6 C
L=2.0 m
Notice that q3 is common to both the terms and comes out of the brackets.
So it turns out the condition for zero force does not depend at all on q3.
Solving the equation:
q2
x
2
q1
=0
2
L x or
L22Lx x 2 q2 = x 2 q1
q 1q 2 x 2 2Lq2 xq 2 L2=0
19
Example 19.1
The quadratic equation
ax 2 bxc=0
has the solutions (two of them)
q 1q 2 x 2 2Lq2 xq 2 L2=0
b± b 2 4ac
x=
2a
has the solutions
2Lq2 ± 4L2 q2 24 q1 q 2 q 2 L2
q 2± q 22 q 1q 2 q2
x=
=
2L
2
q1 q2 2
q 1q 2 2
2
x=
6± 3654 =
6± 90=0.775m
9
9
20