Transcript Chapter 21 Electric Charge and Electric Field

Electricity and Magnetism
Why you should care…
- basis of operation for all electronics
- makes you more marketable
- electric and magnetic forces are the foundation
for almost all physical processes in your daily life
- Formation of solids and liquids
- Sense of touch
- Lots of things
Ch 23.1 – Electric Charges
The electric force is a fundamental force of
nature (like gravity).
The amount of charge a body has determines
its ability to generate electric force.
The amount of charge a body has also determines its ability to ‘feel’
electric force.
No charge? Then no electric force exists.
Charge? Then electric force exists.
Ch 23.1 – Electric Charges
This is really similar to gravity. If two bodies
have mass, they will interact via
gravitational force.
If two bodies have charge, they will interact
via electric force.
The difference? Mass is mass, but there are two types of charge.
Positive Charge – protons.
Negative Charge – electrons.
Charge in the Atom
•
•
•
•
Protons (+)
Electrons (-)
Ions
Polar Molecules
Ch 23.1 – Electric Charges
the Paula Abdul Rule…
Opposite charges attract one another.
Like charges repel one another.
Ch 23.1 – Electric Charges
Most big things in the universe have no net charge.
On a big scale, things usually don’t interact via electric force.
However, charges can be transferred from one object to another, resulting in
net charge.
Ch 23.1 – Electric Charges
Big, important physical principle… Conservation of Charge
In an isolated system, charge is neither created nor destroyed, only
transferred from one place to another
So, when you rub a glass rod on a piece of
silk, friction causes electrons to jump off
the glass and onto the silk.
The silk takes on a net negative charge.
The glass takes on a net positive charge.
Ch 23.1 – Electric Charges
Big, important physical principle… Quantization of Charge
The smallest known packet of charge is the amount stored in one electron.
Robert Millikan (1909) discovered that charge always occurs in integral
multiples of this fundamental amount. Charge is a quantized thing.
We give the special symbol e to represent the absolute
magnitude of the electron’s charge.
- An electron has charge -e
- A proton has charge +e
Bobby Millikan
Ch 23.2 – Induction
Induction is the process of sucking charge off an object without actually
touching it. More in a moment. But first…
Classes of Materials
Conductors
Have ‘free,’ unbound
electrons, which can
move about in the
object.
E.g., metals
Insulators
Can store net charges,
but the charges aren’t
free to move about.
E.g., wood, plastic,
humans
Semiconductors
Can act like conductors
or insulators,
depending on the
conditions.
E.g., silicon, GalliumArsenide, AluminumGallium-Arsenide,
Gallium-Nitride, other
weird alloys.
The process of Induction
Step 1: Start with a neutral conductor.
Step 2: Bring a charged object close. Like
charges repel, opposite charges attract.
Step 3: Provide a reservoir to which free
charges can flow from the conductor. In
electronics, we call this the “Earth” or
“ground.”
Step 4: Remove the earth.
Step 5: You now have a charged conductor.
Yippee, Hooray!
The process of Induction
Step 1: Start with a neutral conductor.
Step 2: Bring a charged object close. Like
charges repel, opposite charges attract.
Step 3: Provide a reservoir to which free
charges can flow from the conductor. In
electronics, we call this the “Earth” or
“ground.”
Step 4: Remove the earth.
Step 5: You now have a charged conductor.
We caused this net charge using induction.
Yippee, Hooray!
The Electroscope
Ch 23.2 – Induction
Charging an object via induction doesn’t require any contact with the object.
In contrast, charging an object via conduction does require contact.
-like rubbing the glass with the silk.
Ch 23.3 – Coulombs’s Law
Coulomb’s Law tells us how the electric force acts.
It’s the electric analog to Newton’s Law of Universal Gravitation.
Charles Coulomb –
(1736-1806) French
physicist famous for
experimenting with the
electric force.
Ch 23.3 – Coulombs’s Law
Coulomb’s Law
Fe  ke
q1 q2
r
2
This is Coulomb’s Law in scalar form.
It tells you the strength of the electric force on one charged object due
to another, but it doesn’t tell you about the direction of the force.
Ch 23.3 – Coulombs’s Law
The magnitude of the
charge on object 1.
Coulomb’s Law
The magnitude of the
force on one particle
due to the other.
Fe  ke
Coulomb’s Constant – a universal
constant that dictates how much
force a given amount will generate.
q1 q2
r
The magnitude of the
charge on object 2.
2
The distance of
separation between the
centers of the two
objects, squared.
Ch 23.3 – Coulombs’s Law
Things to note…
Coulomb’s Law, like Newton’s Law of Gravitation, is an inverse-square law.
The force between to charges gets smaller like the inverse of the square of
the distance between them.
Coulomb’s constant is just that… constant. It always takes value:
ke 
1
4 0
 8.9876109 N  m 2 / C2
The units of charge are called Coulombs. The magnitude of the amount of
Coulombs on a single electron is:
e  1.602181019 C
E.g. 23.1 – The Hydrogen Atom
The electron and proton of a hydrogen atom are separated (on average) by a
distance of about 5.3 x 10-11 m. Find the magnitudes of the electric force
and the gravitational force between the two particles.
Ch 23.3 – Coulombs’s Law
Coulomb’s Law – vector form
Force exerted by object 1
on object 2.

q1q2
F12  ke 2 rˆ12
r
Unit vector pointing from
object 1 to object 2.
Ch 23.3 – Coulombs’s Law
Electric forces follow the law of superposition.
If more than one charge is causing a force on object 1, then the net force
acting on object 1 is just the sum of all the individual forces acting on 1.
 


F1  F21  F31  F41  ...
E.g. 23.2 – Find the Resultant Force
Three point charges are located at the corners of a right triangle, where q1 =
q3 = 5.0 μC, q2 = -2.0 μC, and a = 0.10 m.
Find the resultant force exerted on q3.
E.g. 23.3 – Where is Net Force Zero?
Three point charges lie along the x axis. The positive charge q1 = 15.0 μC is
at x = 2.00 m. The positive charge q2 = 6.00 μC is at the origin. The net
force acting on q3 is zero.
What is the x coordinate of q3?
E.g. 23.4 – Find the Charge on the Sphere
Two identical small charged spheres, each having a mass of 3.0 x 10-2 kg,
hang in equilibrium as shown. The length of each string is 0.15 m, and
the angle θ = 5.0 degrees.
Find the magnitude of the charge on each sphere.
Ch 23.4 – The Electric Field
A more elegant way to think of the same information.
Electric forces arises when one charged object acts on another.
But, imagine if there were only one charged particle in the universe (we’ll
call it the source charge).
Would the source charge’s electrical nature be any different just because it’s
alone?
Ch 23.4 – The Electric Field
In our model, we assume the electric nature of charge is intrinsic to the
existence of charge.
Charge, by virtue of being charge, creates an Electric Field. If you have
charge somewhere in the universe, then you have an electric field.
The effects of a given electric field can be tested by measuring how a
secondary test charge responds to the field.
Ch 23.4 – The Electric Field
In math, we define a source charge’s (q) electric field in terms of the force it
would exert on a test charge (q0) if the test charge were present.
This is a tricky, abstract concept. Think about it.
First, let’s pretend the test charge is in the picture, sitting a distance r away
from the source charge. We can write down the force on the test charge.
From Coulomb’s Law, it’s:

qq
Fe  ke 20 rˆ
r
Ch 23.4 – The Electric Field

qq
Fe  ke 20 rˆ
r
Now, let’s play a trick. Let’s divide the test charge out of the picture.

Fe
qq0
q
ˆ
 ke
r  ke 2 rˆ
2
q0
q0 r
r
 
This is what we call the electric field. It is a measure of the amount of force
exerted per unit of test charge at some point in space.

 Fe
E
q0
Ch 23.4 – The Electric Field
The Electric
Field

 Fe
E
q0
The amount of force
a test charge would
feel at some point in
space.
The amount of charge in the test charge.
Electric Field – The force per unit charge. The electric field is a vector
quantity. It has units of [N/C].
The E-field tells you how much force will be generated per unit charge at
some point in space.
Ch 23.4 – The Electric Field
The Electric
Field

 Fe
E
q0
Things to note…
The electric field exists independently of the test charge.
The existence of the E-field is a property of the source charge.
The test charge serves as a detector of the E-field.
An electric field exists at some point in space if a test charge at that point
experiences an electric force.
Ch 23.4 – The Electric Field
The Electric
Field

 Fe
E
q0


Fe  q0 E
Here’s the point…
Often, we’ll be able to find the electric field at some point in space.
Once we know the E-field, that means we know the force that some charge will
experience at that point in space! This is the power of the electric field theory.
Ch 23.4 – The Electric Field – E-field of a Point Charge
Consider a really small ‘point’ charge, called q.
This charge creates an E-field at all points in space surrounding it.
Let’s put a test charge, q0, at point P, a distance r away from q.
By Coulomb’s Law, q0 will experience a force…

qq0
Fe  ke 2 rˆ
r
… remember, r-hat points from q to q0.
Ch 23.4 – The Electric Field – E-field of a Point Charge
So, the electric field at point P can be found by dividing out q0.

q
E  ke 2 rˆ
r
The E-field a distance
r away from a point
charge, q.
Ch 23.4 – The Electric Field – E-field of a Point Charge
So, the electric field at point P can be found by dividing out q0.

q
E  ke 2 rˆ
r
The E-field a distance
r away from a point
charge, q.
If the source charge is positive, the E-field points away.
If the source charge is negative, the E-field points toward it.
Ch 23.4 – The Electric Field – E-field of a Point Charge

q
E  ke 2 rˆ
r
This field exists regardless of
whether we introduce a test
charge.
The E-field a distance
r away from a point
charge, q.
The electric field is a real
thing. An E-field surrounds
every charged particle in the
universe.
2D representation of a point charge’s vector
E-field. The actual vector E-field extends
radially outward in all 3 dimensions.
Ch 23.4 – The Electric Field
The E-field is a vector thing.
If i point charges generate E-fields at some point in space, the overall E-field
at that point is the algebraic sum of all the individual component fields.

q
Enet  ke  2 rˆi
i ri
The net E-field at point
P due to i point charges.
E.g. 23.5 – Electric Field of a Dipole
Charges q1 and q2 are located on the x axis, at
distances a and b, respectively, from the
origin.
Find the components of the net E-field at
point P, which is on the y axis.
Evaluate the E-field at point P in the special
case that q1  q2 and a  b.
Ch 23.5 – Electric Field of a Continuous Charge Distribution
We know how to find the E-field of a single point charge.
Now, let’s jam a bunch of point charges together. Can we find the E-field they’ll
create?
We’ll pretend the charges are so close to each other that they are basically a
continuous ‘smear’ of charge.
Ch 23.5 – Electric Field of a Continuous Charge Distribution
We’ll consider three cases…
1. Charge continuously packed along a 1-D line. A linear charge density.
2. Charge continuously smeared over a 2-D surface. A surface charge density.
3. Charge continuously spread throughout a 3-D volume. A volumetric charge density.
Ch 23.5 – Electric Field of a Continuous Charge Distribution
A linear charge density.
If a total charge Q is uniformly distributed along a line length l, then the linear charge density, λ,
along the line looks like:
Q

l
Units: C/m
Ch 23.5 – Electric Field of a Continuous Charge Distribution
A surface charge density.
If a total charge Q is uniformly distributed across a surface area, A, then the surface charge density, σ,
across the surface looks like:
Q

A
Units: C/m2
Ch 23.5 – Electric Field of a Continuous Charge Distribution
A volumetric charge density.
If a total charge Q is uniformly distributed throughout a volume, V, then the volumetric charge density,
ρ, throughout the volume looks like:
Q

V
Units: C/m3
Ch 23.5 – Electric Field of a Continuous Charge Distribution
To find the E-field generated by a continuous distribution:
Consider a small amount of charge in the distribution, Δq.
At P, Δq generates an E-field we can find using the point
charge E-field equation…

q
E  ke 2 rˆ
r
The small E-field
generated at P by the
small charge Δq.
Ch 23.5 – Electric Field of a Continuous Charge Distribution
The overall E-field at P will be the sum of all the
contributions from all the little charge bundles in the
orange blob.

qi
E  ke  2 rˆi
ri
i
The net E-field at P due
to all the charge in the
blob.
Ch 23.5 – Electric Field of a Continuous Charge Distribution
The overall E-field at P will be the sum of all the
contributions from all the little charge bundles in the
orange blob.

qi
E  ke  2 rˆi
ri
i
The net E-field at P due
to all the charge in the
blob.
In the limit the chunks
of charge become
infinitesimally small.
qi
dq
rˆi  ke  2 rˆ

2
qi 0
ri
r
i

E  ke lim
E.g. 23.6 – Electric Field of a Charged Rod
A rod of length l has a uniform positive
charge per unit length λ and a total charge
of Q.
Calculate the electric field at a point P that is
located along the long axis of the rod and
a distance a from one end.
E.g. 23.7 – Electric Field of a Charged Ring
A ring of radius a carries a uniformly
distributed positive total charge Q.
Find the E-field due to the ring at a point P
lying a distance x from its center along
the central axis perpendicular to the plane
of the ring.
E.g. 23.8 – Electric Field of a Charged Disk
A disk of radius R has a uniform surface
charge density σ.
Find the E-field at a point P that lies along
the central perpendicular axis of the disk
and a distance x from the center of the
disk.
Ch 23.6 – Electric Field Lines
If we really wanted to know everything about the vector electric field
surrounding a charge, we’d need to draw an infinite number of vectors.
This would be cumbersome.
Drawing Electric Field Lines is easier.
Electric field lines are not the same as the vector electric field. But they do
represent the same information.
Ch 23.6 – Electric Field Lines
Electric Field Lines…
The actual E-field vector always points tangent to the electric field line. The
direction of the electric field line indicates the direction of the actual E-field
vector at that point.
The number of field lines per unit area through a perpendicular surface is
proportional to the magnitude of the E-field in that region.
E-field lines penetrating two surfaces.
The magnitude of the E-field is greater on
surface A than on surface B.
Ch 23.6 – Electric Field Lines
The Rules…
E-field lines always begin on positive charges.
E-field lines always terminate on negative charges.
If there is more positive charge than negative charge in your picture, some
field lines will go out to infinity.
If there is more negative charge than positive charge, some field lines will
come in from infinity and terminate on the negative charge.
Ch 23.6 – Electric Field Lines
The Rules (cont.)…
The number of lines drawn leaving a positive charge (or approaching a
negative charge) is proportional to the magnitude of the charge.
No two field lines will ever cross.
Ch 23.6 – Electric Field Lines
The E-field lines of a symmetrical dipole
Ch 23.6 – Electric Field Lines
The E-field lines of two equal positive charges
Ch 23.6 – Electric Field Lines
The E-field lines of an asymmetrical dipole
Ch 23.7 – Motion of a Charge in a Uniform E-Field
What happens when we place a charge q
of mass m into a uniform E-field?
The E-field causes a force on the charge!
That’s what E-fields do!
Assuming the electric force is the only
force acting on q, then we know:


 Fnet  ma


Fe  ma
But… 
Fe  qE


qE  ma

 qE
a
m
Ch 23.7 – Motion of a Charge in a Uniform E-Field
If the E-field is uniform, the electric force
is constant.
Thus, the acceleration will be constant.
If the q is positive, the mass will accelerate
in the same direction as the E-field.
If the q is negative, the mass will
accelerate against the E-field.

 qE
a
m
E.g. 23.9 – An Accelerating Positive Charge
A uniform E-field is directed along the x axis
between parallel plates of charge
separated by a distance d as shown. A
positive point charge q of mass m is
released from rest at point A and
accelerates to point B.
Find the speed of the particle at B, modeling
it as a particle under constant
acceleration.
Find the speed of the particle at B, modeling
it as a nonisolated system.
E.g. 23.10 – An Accelerating Electron
An electron enters a uniform E-field with vi = 3.00
x 106 m/s and E = 200 N/C. The horizontal
length between the plates is l = 0.100 m.
Find the acceleration of the electron while it is in
the E-field.
Assuming the electron enters the field at t = 0,
find the time at which it leaves the field
Assuming the vertical position of the electron as it
enters the field is yi = 0, what is its vertical
position when it exits the field?