chapter23 elelctric fields

7/29/2019 Chapter23 Elelctric Fields

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Chapter 23

Electric Fields


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Dr. Ghassan Antar 2

Outline

1. Properties of Electric Charges2. Insulators and Conductors

3. Coulombs Law 4. The Electric Field5. Electric Field Lines

6. Conductors in Electrostatic Equilibrium7. Electric Flux and Gausss Law


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Dr. Ghassan Antar 3

Electric Charge: HistoryAs reported by the Ancient Greek philosopher Thales of Miletus around 600 BC, charge (or electricity ) could be accumulated byrubbing fur on various substances, such as amber . The Greeksnoted that the charged amber buttons could attract light objectssuch as hair. (the triboelectric effect).

In 1600 the English scientist William Gilbert returned to thesubject in De Magnete , and coined the New Latin word electricus from (elektron ), the Greek word for " ambe r", whichsoon gave rise to the English words "electric" and "electricity."

In the 18th century it was B. Franklin and W. Watson whoargued in favor of a one-fluid theory of electricity.


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Properties of Electric Charges

Everyday Manifestations:Rubbing a glass rod can deflect a stream of water.Comb attracting bits of paper.

Upon rubbing, these materials become electrically chargedElectric charges are transferred from one material to another.

Electrostatics is thestudy of charges, orcharged bodies, at rest.


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Charge quantification

Charge is quantized (R. Millikan), meaning that chargecomes in integer multiples of the elementary charge e.Q = +/- n e, where

n is any integer ande = 1.602x10 -19 C.

The + sign is for protons and sign is for electrons.

In practice electricity is caused by the mobility of electrons only as protons are very hard to move.

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Sources of electricity

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One looseelectron per atom.It forms thepopulation of freeelectrons in the

material


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Insulators, Conductors and SemiconductorsConductors are materials in which the electric current move

relatively freely through the material. It implies that the outerelectrons of the atoms are loosely bound and free to move throughthe material.

Copper, aluminum and silver are good conductors

Insulators are materials in which no free electric charges exist.Glass, wood and rubber are examples of insulators

The characteristics of semiconductors are in-between those of insulators and conductors (and thus can be controlled).

Silicon and germanium are examples of semiconductors.

Superconductors are materials that do not present any resistance tothe flow of the current.
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/sili.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/solids/sili.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/solids/sili.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/solids/sili.html



Charge conservationElectric charge is always conserved in an isolated system

For example, charge is not created in the process of rubbing twoobjects togetherThe electrification is due to a transfer of charge from one objectto another

A glass rod is rubbed with silk Electrons are transferred from the glassto the silk Each electron adds a negative charge tothe silk An equal positive charge is left on therod



Conductors can be charged by conduction where directcontact is needed to allow the electrons to flow fromone object to another.

Conduction is the movement of electrically charged particlesthrough a transmission medium (electrical conductor).



Conductors can be charged by inductionNo need for physical contact between the objects to be charged.

Ground is something that is connected to the Earth or at the voltage

defined as zero;it is an infinite sink for electrons.

The process of charging a metal (conductor)by Induction



Although the charges (on the electrons) are tightly bound tothe atoms in an insulator they are free to move slightly withinthe atom. This is called polarization.

Insulators can be polarized by induction by charge

rearrangement of the molecules inside the insulator.



The concept of electric field was introduced by

Michael Faraday (1791-1867).

A charge Q creates a FIELD around it called theelectric field which leads to the attraction andrepulsion of another charge placed in its vicinity.

The electric field is to Q what the gravitational fieldg is to mass M .

For a POINT SOURCE :

The Electric Field

r

r

Qk E e 2

r

r r
http://upload.wikimedia.org/wikipedia/commons/8/88/M_Faraday_Th_Phillips_oil_1842.jpg



The Electric Field (cont.)The electric field is defined as the electric force on the test charge per

unit chargeAn electric field is said to exist in the region of space around acharged object; This charged object is the source chargeWhen another charged object, the test charge , enters this electric

field, an electric force acts on itThe electric field is a vector field with SI units of Newtons perCoulomb [N C 1] or in volts per meter [V m 1].
http://upload.wikimedia.org/wikipedia/commons/c/c0/EfieldTwoOppositePointCharges.svg



Test Charge to assess the electric field at a givenpoint in space

A test charge is an imaginary object (usually a point imaginary

particle) that has negligible positive charge so that one can ignore theelectrical field generated by the object itself. This concept is very useful when one wants to understand theproperties of a given electrical field without perturbing it. The existence of an electric field is a property of the source charge

The presence of the test charge is not necessary for the field toexist. The direction of E is that of the force on a positive test charge



Test charge electrically behaves like a real chargebut acts mostly like a detector

http://webphysics.davidson.edu/physlet_resources/bu_semester2/index.html Play: Test Charge

A test charge is positive
http://webphysics.davidson.edu/physlet_resources/bu_semester2/index.htmlhttp://webphysics.davidson.edu/physlet_resources/bu_semester2/index.html



Superposition with Electric Fields and thecontinuous distribution case (I)

The distances between charges in a group of charges may be much

smaller than the distance between the group and a point of interest In this situation, the system of charges can be modeled as continuous The system of closely spaced charges is equivalent to a total charge thatis continuously distributed along some line, over some surface, orthroughout some volume



Superposition with Electric Fields and thecontinuous distribution case (II)

r

r dqk E e 2

Charge densitiesVolume charge density : when a charge is distributed evenly throughout a volume

= Q / V => dq=dV

Surface charge density : when a charge is distributed evenly over a surface area = Q / A => dq= dA Linear charge density : when a charge is distributed along a line

= Q / => dq= l dl



Problem Solving Hints

Units : when using the Coulomb constant, k e, the chargesmust be in C and the distances in mCalculating the electric field of point charges : use thesuperposition principle, find the fields due to theindividual charges at the point of interest and then addthem as vectors to find the resultant field



Problem Solving Hints, cont.

Continuous charge distributions : the vector sums forevaluating the total electric field at some point must bereplaced with vector integrals

Divide the charge distribution into infinitesimal pieces, calculate

the vector sum by integrating over the entire charge distributionUse the charge density to transform the integral over dq into anintegral over space.

Symmetry : take advantage of any symmetry to simplifycalculations



Example Charged Disk The ring has a radius R and auniform charge density Choose dq as a ring of radius r The ring has a surface area

2r dr Replace in the electric fieldexpression

and solve

r

r dqk E e 2



Coulombs Law Charles Augustin de Coulomb (1736-1806)

Angouleme, France.Coulomb used little spheres with differentcharges whose exact value he did not know.Coulomb realized that if a charged sphere touchesanother identical not charged sphere, the charge

will be shared in equal parts symmetrically. Hecould generate charges equal to , , etc., fromthe original charge.Keeping the distance constant between thecharges he noticed that if the charge of one of thespheres was duplicated, the force was alsoduplicated; and if the charge in both spheres wasduplicated, the force was increased to four timesits original value.When he varied the distance between the charges,he found the force decreased in relation to thesquare of the distance.
http://upload.wikimedia.org/wikipedia/commons/4/42/Coulomb.jpg



Coulombs Law: The magnitude

1 2

2eq qF k

r

The magnitude of F is:

directly proportional to the absolute value of each charge ( q1, q2) inversely proportional to square of the separation between theircenters ( r ) The constant of proportion is called the electrostatic constant or

also called the coulomb constant = 1/4pe

0 e 0 is the permittivity of free space

-129 CNm10998 .k e


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The Coulomb Force as a vectorForce is a vector, and it's critical to add

forces as vectors whenever there is morethan one force being exerted.

The sign of the product of q1q2 gives the relative direction of the force between q1 and q2

http://webphysics.davidson.edu/physlet_resources/bu_semester2/index.html (Play:Coulomb 2D)

122

2112 r

r qq

k F e12 21F F
http://webphysics.davidson.edu/physlet_resources/bu_semester2/index.htmlhttp://webphysics.davidson.edu/physlet_resources/bu_semester2/index.htmlhttp://webphysics.davidson.edu/physlet_resources/bu_semester2/index.htmlhttp://webphysics.davidson.edu/physlet_resources/bu_semester2/index.html


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The Superposition Principle

The addition of the different forces exerted by the various

charges is done by summing up the corresponding vectors

F 3

23133 F F F

Consider a two-dimensional situations, all involving the net force the positive charge atthe center of a square experiences because of equal-magnitude charges placed at eachcorner of the square.


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Coulombs force and Electric field

q1

generates an electric field E1

at someposition r.When ANOTHER charge, say q2 isplaced at r , a force between the twocharges occur.This force is equal to the field generatedby q1, that is E 1, multiplied by the chargeq2

F 12=q2E 1

Or E 1=k eq1 / r 2


1 2

2e

q qF k

r


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Summary

State from memory the magnitude and sign of the chargeon an electron and proton and also state the mass of eachparticle.Apply Coulomb's law to determine the magnitude of theelectrical force between point charges separated by a

distance r and state whether the force will be one of attraction or repulsion.Distinguish between an insulator, a conductor, and asemiconductor and give examples of each.

Explain the concept of electric field and determine theresultant electric field at a point some distance from twoor more point charges.Determine the magnitude and direction of the electricforce on a charged particle placed in an electric field.


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Chapter 15 (II)Electric Forces and

Electric Fields


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Outline

1. Properties of Electric Charges2. Insulators and Conductors3. Coulombs Law 4. The Electric Field5. Electric Field Lines


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Electric Field Lines

Electric Field lines were introduced by M. Faraday; They are a convenient way to for visualizing theelectric field pattern; The idea is to draw lines pointing in the direction of the electric field vector at any point.


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Electric Field Lines, GeneralThe density of lines through

surface A is greater than throughsurface BThe magnitude of the electric fieldis greater on surface A than BThe lines at different locationspoint in different directions

This indicates the field is non-uniform

El i Fi ld Li P i i & N i P i


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Electric Field Lines, Positive & Negative PointCharge

The field lines radiate outward in all

directionsIn three dimensions, thedistribution is spherical

The lines are directed away from thesource charge

A positive test charge would berepelled away from the positivesource charge

The field lines radiate inward in

all directionsThe lines are directed toward thesource charge

A positive test charge wouldbe attracted toward the

negative source charge


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Electric Field Lines

http://webphysics.davidson.edu/physlet_resources/bu_semester2/index.html

Play: The electric Field from a dipole.

For multi-poles, the electric field vector, E , is tangent tothe electric field lines at each pointThe number of lines per unit area through a surfaceperpendicular to the lines is proportional to the strength of the electric field in a given region.

Electric field vectors, E , begin on thepositive charge and terminateson the negative charge.No lines can cross each other.

Electric Field Lines Like Charges
http://webphysics.davidson.edu/physlet_resources/bu_semester2/index.htmlhttp://webphysics.davidson.edu/physlet_resources/bu_semester2/index.html


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Electric Field Lines Like Charges

The charges are equal andpositiveThe same number of linesleave each charge since

they are equal in magnitudeAt a great distance, thefield is approximately equalto that of a single charge of 2q


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Electric Field Lines, Unequal ChargesThe positive charge istwice the magnitude of thenegative chargeTwo lines leave the

positive charge for eachline that terminates on thenegative chargeAt a great distance, thefield would beapproximately the same asthat due to a single charge

of + q


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Electric Field Lines, other examples

http://www.falstad.com/vector3de/
http://www.falstad.com/vector3de/http://www.falstad.com/vector3de/


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Electron in a Uniform Field, ExampleThe electron is projectedhorizontally into a uniformelectric fieldThe electron undergoes a

downward accelerationIt is negative, so the acceleration isopposite E

Its motion is parabolic while

between the plates

The electrostatic force vs the gravitational


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The electrostatic force vs. the gravitationalforce

When measured in (such as MKS - see International

System of Units), the Coulomb force constant, k e, isnumerically much larger than the universal gravitationalconstant G . This means that for objects with charge that isof the order of a unit charge (C) and mass of the order of aunit mass (kg), the electrostatic forces will be much larger

than the gravitational forces.The electric force, like gravity, does not require directcontact, it can act at a distance among various objects.Gravity always is attractive whereas the electrostatic force

is repulsive and attractive depending on the charges.Both charges feel the same force, either repulsive orattractive, relative to each other.Both the electric force and gravitation has their amplitudedecrease as 1/ r 2.


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SummaryElectric Field Lines to represent the electricfield.Incorporate the Coulomb field force and theelectric field into the study of the motion of charged particles.Use Newtons law of motion and the kinematicequations to solve problems.


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Suggested Exercises

Conceptual Q: 1, 2, 3, 7, 8, 9Problems: 1, 2, 3, 10, 11, 12, 22, 23, 24, 41, 42,43

chapter23 elelctric fields

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