1.2. Electrostatics_Part 1

7/29/2019 1.2. Electrostatics_Part 1

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UG20.02

Electromagnetism and Optics I

3(2-1)

SAITM AIT Program

B.Sc. in Engineering in (ICT/ Mechatronics/ Electronics)

Department of Mechatronics,

Faculty of Engineering,

South Asian Institute of Technology and Management (SAITM)


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Topics Covered by week by week

Week 1 and 2: (chapter 16, pg. 439)

Electrostatics,

electric current and electric force,

Kirchhoff's laws and linear circuits,

Electric charge,

Coulomb's law,

Electric fields, field lines and forces.

January 2010 2ICT 1102 - Electromagnetism and Optics I


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Topics Covered by week by week

Week 1 and 2:

Electric dipoles,

Electric flux,

Gauss's law,

Electric potential and potential energy,

Potential difference and gradient, Capacitance,

Series and parallel.

Energy storage

January 2010 3ICT 1102 - Electromagnetism and Optics I


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Static electricity; electric charge and its

conservation

The word electricity comes from the Greek wordElectron, which means amber (variant of treeresin, If you rub on a cloth it will attack smallleaves)

A piece of hard rubber, a glass rod, or a plasticruler rubbed with a cloth will also display thisamber effect or static electricity as we call ittoday

An object becomes charged as a result ofrubbing, and is said to posses a net electriccharge


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conservation

There are two types of electric charge

Each type of charge repels the same type butattracts the opposite type

That is unlike charges attracts

Like charges repel

Benjamin Franklin named them as Positive

and Negative Charge on rubbed glass rod is positive

Charge on rubbed plastic ruler is negative


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conservation

Franklin said that Whenever a certain amount of charge is produced on

one object, an equal amount of the opposite type ofcharge is produced on another object

So during any process, the net change in the amountof charge produced is zero

The law of conservation of electric charge The net amount of electric charge produced in any

process is zero Or in another way: no net electric charge can be

created or destroyed


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Electrical charge in atom

Simplified model of an atom Tiny, heavy, positively charged

nucleus surrounded by one ormore negatively charged

electrons Nucleus contains protons

(positively charged) and neutrons(no net electric charge)

Ion: atom with net positive ornegative charge By losing its electrons

Or by gaining more electrons


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In solid materials,

Nuclei tend to remain close to fixed positions

Some electrons may move quite freely

When an object is neutral, it contains equalamounts of positive and negative charge

Charging of an object by rubbing

Transfer of electrons from one object to the other Hold their charge only for a limited time and

eventually return to the normal state


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Charge leaks-off into water molecules in air

Because, water molecules are polar Neutral but charge is not distributed uniformly

Extra electrons on object are attracted to positive end of

water molecules Positively charged objects attract electrons from water

molecules

In liquids and gases, nuclei or ions can move aswell as electrons


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Insulators and conductors

Conductors: materials like iron, metals are goodconductors

Non conductors (insulators): wood, rubber

Semiconductors: silicon, germanium


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Insulators and conductors

In an insulating material, electrons are bound very tightly tonuclei

In a good conductor, some of the electrons are bound veryloosely, can move about freely (cannot leave object easily)within the material (free electrons or conductionelectrons)

When a positively charged object is brought close to ortouches a conductor, the free electrons in the conductorare attracted by this positively charged object and movequickly toward it Free electrons move away from a negatively charged object

In a semiconductor very fewer free electrons, in a insulatoralmost none


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Induced charge; the electroscope

Scenario 1: A positively chargedmetal object is brought close toan uncharged metal object If the two touch, free electrons in

neutral one are attracted to the

positively charged object andsome will pass over it

Now the originally neutral objecthave a net positive charge

This process is called charging by

conduction or by contact Two objects end up with same

sign of charge


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Scenario 2: positively charged object isbrought close to a neutral rod, butdoes not touch it Free electrons does not leave the rod,

but move within the metal towards the

external positive charge, leaving positivecharge at the opposite end of the rod

Charge is said to have induced at twoends of rod

No net charge has created in the rod

Charges have been separated

If the metal is broken in to two, twocharged objects will be created, onecharged (+)vely and other (-)vely


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Scenario 3: First connect the metal object with a

conducting wire to the ground

Object is grounded or earthed

Earth is so large, so it can, Conduct, accept or give up electrons

Acts like a reservoir of charge

Now metal is positively charged, ifwire is cut, object will have positiveinduced charge on it

What will happen if we cut the wireafter we move away the negativelycharged object?


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Charge separation can also be

done in non conductors

Almost no electrons can move

freely within the non conductor

They can move slightly within

their own atoms and molecules

Non conductor as a whole isattracted to the external

positive charge


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The electroscope

A device that can be used fordetecting charge

Two movable metal leaves, often madeof gold

Connected to outside metal knob by aconductor

Insulated casing

Identifying the sign of the charge

First charge with a known sign byconduction

Now modern electrometers are used

http://en.wikipedia.org/wiki/Electrometer
http://en.wikipedia.org/wiki/Electrometerhttp://en.wikipedia.org/wiki/Electrometer


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The electroscope


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Coulombs Law

Electric charge exerts aforce of attraction orrepulsion on other electric

charges What factors affect the

magnitude of this force

French physicist Charles

Coulomb investigatedelectric forces using torsionbalance


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Coulombs Law

k = proportionality constant

Gives the magnitude of the electric force that either objectexerts on the other

Direction of the electric force is always along the linejoining the two objects Equal signs repel each other

Opposite signs attract each other


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Coulombs Law

SI unit: coulomb (C)

k = 8.988 * 109Nm2/C2 or

k 9.0 * 109Nm2/C2

1 C = amount of chargewhich, if placed on each oftwo point objects that are 1

m apart, will result in eachobject exerting a force of 9 *109 N on the other


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Coulombs Law

Charge on one electron is the smallest charge

found in nature, called e (elementary charge)

e = 1.602 * 10-19 C

Charge on electron is -e, charge on proton is

+e

Electric charge is quantized (existing only on

discrete amounts: 1e, 2e, 3e, etc)


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Coulombs Law

o = permittivity of free space

These equations apply to objects whose size is much smaller thanthe distance between them

Ideally precise for point charges (spatial size negligible compared toother distances)

r is basically the distance between their centers

Here we talk only about stationary charges (electrostatics)

When using the Coulombs law determine the direction of forcebased on force is attractive or repulsive


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Coulombs Law

Gives the force on a charge due to only one

other charge

If several charges are present?

The net force on any one of them will be the

vector sum of the forces on that charge due to

each of the others (principle of superposition)


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Solving problems involving coulombs

law and vectors Electric force between charged particles at rest (electrostatic force

or Coulomb force) is a vector

Vector addition methods

Tail-to-tip method

Parallelogram method

Adding components method (precise and easy to use)

Common practices

F31 : Force exerted on particle 3 by particle 1

Draw diagram, showing all the forces acting on objects First find the magnitude using the equation

Then find the direction by comparing charges

l bl l l b


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Solving problems involving coulombs

law and vectors


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The electric field

Many forces referred to ascontact forces Pushing or pulling a cart

Tennis racket hitting a tennis ball

Gravitational and electric forceacts at a distance, how can weexplain this? By using the idea of a field by

Michael Faraday

Electric field extends outwardfrom every charge and permeatesall of space


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The electric field

To investigate the electric field we will use a

small positive test charge

so small that the force it exerts does not

significantly alter the distribution of those othercharges that create the field


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The electric field

Electric field is defined in terms of the force onsuch a positive test charge

Electric field E at any point in the space = theforce F exerted on a tiny positive test charge

placed at that point divided by the magnitude ofthe test charge q,

E is a vector, Direction is direction of the force

Magnitude is the force per unit charge

SI unit: Newtons per Coulomb (N/C)


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The electric field

E is independent of the test charge q

Above equations are referred to aselectric field form of Coulombs law

If electric field (E) is given at a point,force on a charge can be calculated, Valid even if q is not small

If q is positive F and E are in same

direction If q is negative F and E are in opposite

directions


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The electric field

Electric field E due to a,

Positive charge, points away from the charge

Negative charge, points towards that charge

Electric field due to more than one charge, the

individual fields due to each charge are added

vectorially (superposition principle)


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Field lines

Since electric field isvector, sometimes referas a vector field

Drawing field usingvector lines (magnitudeand direction) atdifferent points is

confusing

Solution is field lines


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Field lines

To visualize the electric field we draw series of lineselectric field lines (lines of force) indicate thedirection of the force due to the given field on apositive test charge

Point outward from a single isolated positive charge Point inward towards a single isolated negative charge

Starting from positive and ending at negative

Number of lines starting on a positive charge or ending ona negative charge is proportional to the magnitude of the

charge The closer together the lines are, the stronger the electric

field in that region

Number of lines crossing unit area perpendicular to E isproportional to the magnitude of the electric field


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Field lines


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Properties of Field lines

1. Electric field lines indicate the direction of the electricfield; the field points in the direction tangent to thefield line at any point

2. The lines are drawn so that the magnitude of the

electric field, E, is proportional to the number of linescrossing unit area perpendicular to the lines. Thecloser together the lines, the stronger the field

3. Electric field lines start on positive charges and endon negative charges; and the number of starting or

ending is proportional to the magnitude of the charge Note that field lines never cross (cannot have two

directions at the same point)


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Electric fields and conductors

Electric field inside a

conductor is zero in the

static situation

Any net charge on a

conductor distributes itself

on the surface


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Electric fields and conductors

Electric field is always

perpendicular to the

surface outside of a

conductor


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Gausss Law

Important relation in electricity

Developed by Karl Friedrich Gauss(1777-1855)

Relates electric charge and electricfield

More general version of Coulombslaw

Electric flux = electric field passingthrough a given area

Flux through an area is proportional tothe number of lines passing thoughtthat area


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Gausss Law

Involves total flux through a

closed surface

Sum is over any closed surface

Qenc : net charge enclosed

within the surface


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Gausss Law

Electric field is zero inside a empty sphere or a

conductor

Electric field between two parallel plates


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Photocopy machines and computer

printers Photocopy machines and laser printers Photocopier

Lenses and mirrors focus image of the original onto drum

Drum is good conductor (Al), coated with selenium has photoconductivity property

Electrical non conductor in dark, conductor at light

Steps Place positive charge on selenium later

Image is projected to drum, at lighter areas selenium becomesconductive and neutralize

Toner with negative charge is brushed on to drum Presses drum against a paper

Paper is heated to fix toner particles

In a color copier this is repeated for each color


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Photocopy machines and computer

printers

Laser printer

Instead of hardcopy a softcopy is used as the input

Use a laser beam

Inkjet printer

Use a nozzle to spray tiny droplets of ink


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Summary

Electrostatics, electric current and electric force,

Kirchhoff's laws and linear circuits,

Electric charge, Coulomb's law,

Electric fields, field lines and forces,

Electric dipoles,

Electric flux, Gauss's law.

Documents

1.2. Electrostatics_Part 1