Transcript Coulomb and Stuff - The Burns Home Page

SPH4U
Electric Forces
Mr. Burns
Maxwell’s Equations

E 
0
Gauss’s Law: The electric field’s mapping is equal to the
charge density divided by the permittivity of free space.
The relationship between electric field and electric charge
B  0
Gauss’s Law for Magnetism: The net magnetic flux out
of any closed surface is zero. There is no such thing as
a magnetic monopole
B
 E  
t
We can make an electric field by changing a magnetic
field
  B  u0 J   0  0
E
t
We can make a magnetic field with a changing electric
field or with a current
c
1
 0 0
Maxwell’s
st
1
Equation.

E 
0
Maxwell’s first equation is Gauss’s Law. This equation tells us that
electric field lines (E) DIVERGE outward from positive charges and
CONVERGE inward to the negative charges.
Maxwell’s
nd
2
Equation.
B  0
Maxwell’s second equation tells us that the magnetic field (B) never
DIVERGES or CONVERGE. They always go around in closed loops,
therefore there doesn’t exist a single magnetic pole.
Maxwell’s
rd
3
Equation.
B
 E  
t
Maxwell’s third equation is Faraday’s Law. This equation tells us that
electric field lines (E) CURL around changing magnetic fields (B) and
that changing magnetic fields induce electric fields.
Maxwell’s
  B  u0 J   0  0
th
4
Equation.
E
t
Maxwell’s fourth equation tells us that the magnetic field (B) lines CURL
around electric currents AND that magnetic field (B) lines CURL around
changing electric fields.
The Origin of Electricity
The electrical nature of matter is inherent
in atomic structure.
mp  1.6731027 kg
mn  1.6751027 kg
me  9.111031 kg
19
e  1.6010 C
coulombs
The Origin of Electricity
In nature, atoms are normally
found with equal numbers of protons
and electrons, so they are electrically
neutral.
By adding or removing electrons
from matter it will acquire a net
electric charge with magnitude equal
to e times the number of electrons
added or removed, N.
q  Ne
The Origin of Electricity
Example 1 A Lot of Electrons
How many electrons are there in one coulomb of negative charge?
q  Ne
q
1.00 C
18
N 

6
.
25

10
e 1.60 10 -19 C
Charged Objects and the Electric Force
It is possible to transfer electric charge from one object to another.
The body that loses electrons has an excess of positive charge, while
the body that gains electrons has an excess of negative charge.
Charged Objects and the Electric Force
LAW OF CONSERVATION OF ELECTRIC CHARGE
During any process, the net electric charge of an isolated system remains
constant (is conserved).
Charged Objects and the Electric Force
Like charges repel and unlike
charges attract each other.
Lightning
Conductors and Insulators
Not only can electric charge exist on an object, but it can also move
through an object.
Substances that readily conduct electric charge are called electrical
conductors.
Materials that conduct electric charge poorly are called electrical
insulators.
Charging by Contact and by Induction
Charging by contact.
Charging by Contact and by Induction
Charging by induction.
Charging by Contact and by Induction
The negatively charged rod induces a slight positive surface charge
on the plastic.
Coulomb’s Law
Physicists did not like the concept of
“action at a distance” i.e. a force that
was “caused” by an object a long
distance away
They preferred to think
of an object producing
a “field” and other
objects interacting with
that field
they liked to think...
Thus rather than ...
-
+
-
+
Coulomb’s Law
Coulomb’s Law
COULOMB’S LAW
The magnitude of the electrostatic force exerted by one point charge
on another point charge is directly proportional to the magnitude of the
charges and inversely proportional to the square of the distance between
them.
F k
q1 q2
  8.851012 C2 N  m2 
r2
k  1 4o   8.99109 N  m2 C2
Coulomb’s Law
Example 3 A Model of the Hydrogen Atom
In the Bohr model of the hydrogen atom, the electron is in orbit about the
nuclear proton at a radius of 5.29x10-11m. Determine the speed of the
electron, assuming the orbit to be circular.
F k
q1 q2
r2
Coulomb’s Law
F k
q1 q2
r2
8.9910

9

N  m 2 C 2 1.601019 C
5.2910
11
m


2
2
 8.22108 N
F  mac  mv2 r
v  Fr m 
8.2210 N5.2910
8
9.1110-31 kg
11
m
  2.1810 m s
6
Coulomb’s Law
Electrostatics
Gravitational Force
Two types of charges (q):
positive and negative
One type of mass (m): positive
mass
Attraction (unlike charges) and
repulsion (like charges)
Attraction (all masses)
F: F  k q1q 2
2
F:
Potential energy:
Potential energy:
r
k  8.99  109 N  m 2 / C 2
q1q 2
PE  k
r
m1m 2
FG
r2
G  6.67  1011 N  m 2 / kg2
m1m 2
PE  G
r
Coulomb’s Law
Gravitational vs. Electrical Force
F
q1
m1
q1q2
Felec  k 2
r
m1m2
Fgrav  G 2
r
F
r
G  6.67 1011
N  m2
kg 2
q2
m2
Felec q1q2 k
Fgrav m1m2 G
2
N

m
k  8.99 109
C2
For an electron:
* q = 1.6  10-19 C
m = 9.1  10-31 kg
Felec 
 42

17
4.
10
Fgrav
* smallest charge seen in nature!
Coulomb’s Law

Suppose your friend can push their arms apart with
a force of 450 N. How much charge can they hold
outstretched?
2m
F= 450 N
kQ 2
F 2
r
Qr
+Q
F
450
 2
k
9 109
= 4.47•10-4 C
4.47 10-4 
1e
15

2.8

10
e
19
1.6 10 C
31
9.1

10
kg
2.8 1015 e 

e
2.54 1015 kg
That’s smaller than one cell in your body!
-Q
Coulomb’s Law
Example 4 Three Charges on a Line
Determine the magnitude and direction of the net force on q1.
Coulomb’s Law
F12  k
F13  k
q1 q2
r
2
q1 q3
r
2
8.9910

9
8.9910







N  m 2 C2 3.0 106 C 4.0 106 C
0.20m2
9
N  m 2 C2 3.0 106 C 7.0 106 C
0.15m2
 

F  F12  F13  2.7 N  8.4N  5.7N
 2.7 N
 8.4 N
Coulomb’s Law
Coulomb’s Law
F42
Find the net force
exerted on the point
charge q2.
F32
F12
F42
F net
d 2
y
x
F32
F12




Fnet  F12  F32  F42
Coulomb’s Law
The Electric Field
The positive charge experiences a force which is the vector sum of the
forces exerted by the charges on the rod and the two spheres.
This test charge should have a small magnitude so it doesn’t affect
the other charge.
The Electric Field
Example 6 A Test Charge
The positive test charge has a magnitude of
3.0x10-8C and experiences a force of 6.0x10-8N.
(a) Find the force per coulomb that the test charge
experiences.
(b) Predict the force that a charge of +12x10-8C
would experience if it replaced the test charge.
(a)
(b)
F 6.0 108 N

 2.0 N C
8
qo 3.0 10 C


F  2.0 N C 12.0 108 C  24108 N
The Electric Field
DEFINITION OF ELECTRIC FIELD
The electric field that exists at a point is the electrostatic force experienced
by a small test charge placed at that point divided by the charge itself:
F

qo
The strength of the
electric field can be
thought of as the ratio
of the force on that
charge and the test
charge itself
SI Units of Electric Field: newton per coulomb (N/C)
The Electric Field
It is the surrounding charges that create the electric field at a given point.
The Electric Field
Electric fields from different sources
add as vectors.
The Electric Field
Example 10 The Electric Field of a Point Charge
The isolated point charge of q=+15μC is
in a vacuum. The test charge is 0.20m
to the right and has a charge qo=+0.8μC.
Determine the electric field at point P.

 F
E
qo
F k
q1 q2
r2
The Electric Field
F k
q qo
r2
8.99 10


E
9
N  m 2 C2 15 106 C
 0.20m 
 0.80 10
2
F
2.7 N

 3.4 106 N C
-6
qo 0.8010 C
6
C

 2.7N
The Electric Field
q qo 1
F
E
k 2
qo
r qo
The electric field does not depend on the test charge.
Point charge q:
Ek
q
r2
The Electric Field
Example 11 The Electric Fields from Separate Charges May Cancel
Two positive point charges, q1=+16μC and q2=+4.0μC are separated in a
vacuum by a distance of 3.0m. Find the spot on the line between the charges
where the net electric field is zero.
Ek
q
r2
The Electric Field
Ek
q
r2
E1  E 2


1610 C
4.0 10 C
k
k
6
d2
6
3.0m  d 
2
4.0  3.0m  d   d 2
2
d  2.0 m
The Electric Field
Conceptual Example 12 Symmetry and the
Electric Field
Point charges are fixes to the corners of a rectangle in two
different ways. The charges have the same magnitudes
but different signs.
Consider the net electric field at the center of the rectangle
in each case. Which field is stronger?
The Electric Field
THE PARALLEL PLATE CAPACITOR
charge density
Parallel plate
capacitor
E
q
 V
 
o A o
d
Change in
potential
(voltage)
Distance
between
plates
  8.851012 C2 N  m2 
Electric Field Lines
Electric field lines or lines of force provide a map of the electric field
in the space surrounding electric charges.
Electric Field Lines
Electric field lines are always directed away from positive charges and
toward negative charges.
Electric Field Lines
Electric field lines always begin on a positive charge
and end on a negative charge and do not stop in
midspace.
Electric Field Lines
The number of lines leaving a positive charge or entering a
negative charge is proportional to the magnitude of the charge.
Electric Field Lines
Electric Field Lines
Conceptual Example 13 Drawing Electric
Field Lines
There are three things wrong with part (a) of
the drawing. What are they?
The Electric Field Inside a Conductor: Shielding
At equilibrium under electrostatic conditions, any
excess charge resides on the surface of a conductor.
At equilibrium under electrostatic conditions, the
electric field is zero at any point within a conducting
material.
The conductor shields any charge within it from
electric fields created outside the conductor.
The Electric Field Inside a Conductor: Shielding
The electric field just outside the surface of a conductor is perpendicular to
the surface at equilibrium under electrostatic conditions.
Flash – Coulombs Law
Flash – Electric Forces