PHYSICS - Electrostaticscottageschoolphysics.weebly.com/uploads/1/0/2/7/...Jan 19, 2017 · PHYSICS - Electrostatics. Electrostatics, or electricity at rest, involves electric charges,

PHYSICS - Electrostatics

Electrostatics, or electricity at rest, involves electric charges, the forces between them, and their behavior in materials.

The fundamental rule at the base of all

electrical phenomena is that

like charges repel

and

opposite charges attract.

22.1 Electrical Forces and Charges

The helium nucleus is composed of two protons and

two neutrons. The positively charged protons attract

two negative electrons.



An object that has unequal numbers of

electrons and protons is electrically charged.

22.2 Conservation of Charge

A charged atom is called an ion.

• A positive ion has a net positive charge; it has lost

one or more electrons.

• A negative ion has a net negative charge; it has

gained one or more extra electrons.


• Innermost electrons tightly bound to the nucleus.

• Outermost electrons are bound very loosely.

• How much energy is required to tear an electron away

from an atom varies for different substances.


When electrons are

transferred from the fur to the

rod, the rod becomes

negatively charged.


Electric Charge is Quantized


● Any object that is electrically charged has an excess

or deficiency of some whole number of electrons.

● This means that the charge of the object is a whole-

number multiple of the charge of an electron.

Electrons are neither created nor destroyed but are

simply transferred from one material to another. This

principle is known as conservation of charge.


If you scuff electrons onto your shoes while walking

across a rug, are you negatively or positively

charged?

22.2 Check Question

Coulomb’s law states that (for charged particles or

objects that are small compared with the distance

between them), the force between the charges varies…

… directly as the product of the charges and…

… inversely as the square of the distance between

them.

22.3 Coulomb’s Law

Recall from Newton’s law of gravitation...


For charged objects...

Where:

d is the distance between the charged particles.

q1 represents the quantity of charge of one particle.

q2 is the quantity of charge of the other particle.

k is the proportionality constant.


The SI unit of charge is the coulomb, abbreviated C.

A charge of 1 C is the charge of 6.24 × 1018 electrons.


The Electrical Proportionality Constant

The proportionality constant k in Coulomb’s law is

similar to G in Newton’s law of gravitation.

k = 9,000,000,000 N·m2/C2 or 9.0 × 109 N·m2/C2



Because most objects have almost exactly equal

numbers of electrons and protons, electrical forces

usually balance out.

Between Earth and the moon, for example, there is no

measurable electrical force.

In general, the weak gravitational force, which only

attracts, is the predominant force between astronomical

bodies.


• Materials through which electric charge can flow

are called conductors.

• Metals are good conductors for the motion of

electric charges because their electrons are

“loose.”

22.4 Conductors and Insulators

• Electrons in other materials—rubber and glass,

for example—are tightly bound and remain with

particular atoms.

• They are not free to wander about to other

atoms in the material.

• These materials, known as insulators, are poor

conductors of electricity.


In power lines, charge flows much

more easily through hundreds of

kilometers of metal wire than

through the few centimeters of

insulating material that separates

the wire from the supporting

tower.


• Semiconductors are materials that can be

made to behave sometimes as insulators and

sometimes as conductors.


• Superconductors are materials that at certain low

temperatures acquire zero resistance to the flow of

charge.


Two ways electric charge can be transferred are

➔ by friction

➔ by contact

22.5 Charging by Friction and Contact

• Electrons can be transferred from one material to another

by simply touching.

• When a charged rod is placed in contact with a neutral

object, some charge will transfer to the neutral object.

• This method of charging is called charging by contact.

22.5 Charging by Friction and Contact

If a charged object is brought near a conducting

surface, even without physical contact, electrons will

move in the conducting surface. This is called

charging by induction.

22.6 Charging by Induction


The charge on the spheres has been redistributed, or induced.



Charge Induction by Grounding










When we touch the metal surface with a finger, charges

that repel each other have a conducting path to a

practically infinite reservoir for electric charge—the

ground.

When we allow charges to move off (or onto) a

conductor by touching it, we are grounding it.


Charging by induction occurs

during thunderstorms.


• The primary purpose of the

lightning rod is to prevent a

lightning discharge from

occurring.

• If lightning does strike, it may be

attracted to the rod and short-

circuited to the ground, sparing

the building.


Lightening Rods

How an Electrophorus Works

Charge polarization can occur in insulators that are

near a charged object.

22.7 Charge Polarization

a. When an external negative charge is brought closer

from the left, the charges within a neutral atom or

molecule rearrange.


a. When an external negative charge is brought closer

from the left, the charges within a neutral atom or

molecule rearrange.

b. All the atoms or molecules near the surface of the

insulator become electrically polarized.




Electric Dipoles

Many molecules—H2O, for

example—have a little more

negative charge on one side

of the molecule than on the

other.

Such molecules are said to be

electric dipoles.


In summary, objects are electrically charged in three ways.

• By friction, when electrons are transferred by friction

from one object to another.

• By contact, when electrons are transferred from one

object to another by direct contact without rubbing.

• By induction, when electrons are caused to gather or

disperse by the presence of nearby charge without

physical contact.


You can sense the force field that surrounds a

charged Van de Graaff generator.

22.8 Electric Fields


gThe distance

between field lines

indicates

magnitudes.


FG = mg

FG

22.9 Electric Field Lines

EE


FG = mg

FG

FE = qE

FE

The direction of an electric field at any point, by

convention, is the direction of the electrical force on

a small positive test charge placed at that point.


a. The field lines around a single positive charge extend to infinity.



b. For a pair of equal but opposite charges, the field lines emanate

from the positive charge and terminate on the negative charge.



b. For a pair of equal but opposite charges, the field lines emanate

from the positive charge and terminate on the negative charge.

c. Field lines are evenly spaced between two oppositely charged

capacitor plates.


22.9 Uniform Electric Fields

Between two parallel plates containing equal but

opposite charges, the electric field is uniform.

Both the magnitude and direction of the field is the

same at all points between the plates.

+ + + + + +

+ + +

- - - - - -

- - -

E

22.9 Uniform Electric Fields

+ + + + + +

+ + +

- - - - - -

- - -

E+

-

q

qFE

FE

FE= qE

22.9 Example

+ + + + + +

+ + +

- - - - - -

- - -

-oil

drop

FE

FG

Robert Millikan determined the charge on an electron by suspending

negatively charged oil drops in a uniform electric field created by two charged

plates. Determine the charge on the oil drop in terms of its mass (m), the

electric field (E) and the gravity of Earth (g).

22.9 Example

When an electron is released from rest in a uniform electric field E,

it reaches a velocity of v after traveling a distance of x. In terms of

v, what will be the electron’s velocity if the magnitude of the electric

field is doubled while traveling the same distance?

22.9 Electric Fields of Point Charges

So far we have two equations for the electrical force:

FE= qE AND

As with gravity, we can set these equal to each other and solve

for E to determine the strength of the electric field at a given

position. The result should look very familiar from our study of

gravity...

22.9 Electric Fields of Point Charges

22.9 Example

A conducting sphere contains a charge q. The electric field at a set

distance from the center of the sphere is E. If the charge on the

sphere and the distance from the sphere are both doubled, by what

factor would the electric field change?

22.9 Superposition of Electrical Fields

A +8 coulomb charge is located 2 meters to the left of the origin. A

-4 coulomb charge is located 2 meters to the right of the origin.

Determine the magnitude and direction of the electric field at point

P located at the origin.

+

8 C P 4C

-

-2 -1 0 1 2

22.9 Superposition of Electrical Fields

Two negative charges, 4 coulombs and 16 coulombs, are

separated by a distance of 1 meter. Determine the location, as

measured from the 4-coulomb charge, where the electric field is

zero.

-

4 C 16C

-

1 meter

22.10 Electric Shielding

Consider a charged metal sphere.

Because of repulsion, electrons

spread as far apart as possible,

uniformly over the surface.

A positive test charge located exactly

in the middle of the sphere would feel

no force. The net force on a test

charge would be zero.



How to Shield an Electric Field

There is no way to shield gravity, because gravity

only attracts. Shielding electric fields, however, is

quite simple.

• Surround yourself or whatever you wish to

shield with a conducting surface.

• Put this surface in an electric field of whatever

field strength.

• The free charges in the conducting surface will

arrange on the surface of the conductor so that

fields inside cancel.


22.11 Electrical Potential Energy

• Imagine moving multiple

charges from A to B. For

each charge we move,

there is a gain in PE.

• So it makes sense to talk

about difference in

potential energy per

charge.


Difference in potential energy per charge

POTENTIAL DIFFERENCE

ELECTRIC POTENTIAL

VOLTAGE


Difference in potential energy per charge

Joules

Coulomb


1 Joule / Coulomb = 1 Volt





V = Ed

CAUTION: This equation is only for uniform electric fields. For

example, for the field between two parallel charged plates.

E = V

d

Electric potential

is not the same as

electrical potential energy.

Electric potential is

electrical potential energy per charge.

22.12 Electric Potential


If there were twice as much charge on one of the

objects, would the electrical potential energy be the

same or would it be twice as great? Would the

electric potential be the same or would it be twice as

great?


22.12 Example

d

P

+ + + + +

- - - - - -

6 V

4 V

2 V

0 V

-+

22.12 Example

Two charged plates with a 20 newton per coulomb

electric field are separated by a distance of 10

centimeters. A proton is located at the midpoint

between the plates.

A) Determine the potential difference between the

charged plates.

B) Determine the potential acting on the proton.

22.12 Potential of Point Charges

+q

E

6 V

4 V

2 V

V = kq

r

E = kq

r2

22.12 Example

A +4 coulomb charge is located 4 meters to the left of

the origin. A -4 coulomb charge is located 4 meters

to the right of the origin. Determine the electric

potential at point P located at the origin.

22.12 Electric Potential Energy

UE = qV

Once we know the electric potential of a point in

space, it’s easy to find the electric potential energy of

any amount of charge.

Since V is simply difference in potential energy PER

CHARGE, we only need to multiply by how much

charge we have to find the total potential energy.

22.12 Work of Electricity

WE = 𝚫K = -𝚫UE = -q𝚫V = -q (Vf - Vi)

|W | = |q| ● |(Vf - Vi)|

22.12 Example

The diagram above shows the equipotential lines in a

region of space. Determine the work done on a 2-

coulomb charge that is moved from point A to point

B.

-4 V -2 V 0 V 2 V 4 V 6 V

+

AB

22.12 Conservation of Energy

Don’t forget that you can still apply what you already

know about energy to solve electric potential problems.

See below:

-

-

-

+

+

+

-

Two charged plates have a

potential difference of V. An

electron of mass m and charge

e is initially at the negative plate.

It accelerates through the

potential difference. Determine

the electron’s max speed, v, in

terms of the given variables.

22.13 Electrical Energy Storage

A capacitor is a

device that can

store electrical

energy.

22.13 Electrical Energy Storage

22.13 Capacitance

Capacitance, C, is measured in farads (F) and is a

measure of the ability of a capacitor to store charge and

energy.

Capacitance is proportional to the area of one of the

plates, A and inversely proportional to the distance of the

plate separation, d.

Epsilon is a constant known as the permittivity of free

space and = 8.85 x 10-12 C2/Nm2

22.13 Capacitance

Other formulas you might need for capacitance:

22.13 Capacitance

Other formulas you might need for capacitance:

UC =

22.14 The Van de Graaff Generator

22.14 The Van de Graaff Generator

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PHYSICS - Electrostaticscottageschoolphysics.weebly.com/uploads/1/0/2/7/...Jan 19, 2017 · PHYSICS - Electrostatics. Electrostatics, or electricity at rest, involves electric charges,