Electrostatics - folk.uio.nofolk.uio.no/ravi/cutn/elec_mag/3_electrostatics2.pdf · Electrostatics: Coulomb’s Law The INSTRUMENT: The torsion balance P.Ravindran, PHY041: Electricity

ElectrostaticsElectrostatics

P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics1

Electrostatics: Coulomb’s LawThe MAN: Charles Augustin de CoulombThe MAN: Charles Augustin de Coulomb

He was born in 1736 in AngoulêmeHe was born in 1736 in Angoulême, France.

He received the majority of his higherHe received the majority of his higher education at the Ecole du Genie at Mezieres (sort of the French equivalent of universities like Oxford, Harvard, etc.) from , , )which he graduated in 1761.

He then spent some time serving as a military engineer in the West Indies and other French outposts, until 1781 when he was permanently stationed in Paris and was able to devote more time to scientific research. Between 1785‐91 he published seven memoirs (papers) on physics.

P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics

Electrostatics: Coulomb’s LawThe INSTRUMENT: The torsion balance


Coulomb’s torsion balanceand how it worksand how it works

Coulomb used a torsion balance to measure electrostatic force.electrostatic force.

Inside the balance are two pith balls. One is mounted on the end of a glass rod and is unmovable (red), the other can spin around (blue).

When the two pith balls are given an electrostatic charge (charging a plastic rod by rubbing it with furcharge (charging a plastic rod by rubbing it with fur then touching that rod to the pith ball) the mobile ball will move away from the stationary one if both receive the same charge (positive or negative); or will move towards the unmovable ball, if each is given a different charge The distance the mobile ball movesdifferent charge. The distance the mobile ball moves is used to measure the electrostatic force.

Coulomb was able to measure the torsion on the fiber with the scale near the top of the device and the distance between the balls on the scale wrapped

d h b f h j H d i d h i lpp

around the base of the jar. He derived a mathematical equation that described the relationship between these two measurements.

Coulomb’s Law states: The force between two Coulomb s Law states: The force between two small charged spheres is proportional to the magnitude of either charge and inversely proportional to the square of the distance between centers.


e ee e e

Coulomb’s law

Coulomb’s Law: The magnitude of the force between two point h i ti l t thcharges is proportional to the product of their charges and inversely proportional to theinversely proportional to the square of their separation.

0 = 8.854 x 10‐12 C2N‐1m‐2 “electric permittivity”

k 9 2 2 k 1/4k = 8.988 x 109 C‐2Nm2 k = 1/4π 0

Measured charge on the electron: e = 1.6 x 10‐19 C


Coulomb’s LawCoulomb s Law

FormulaFormula

Where F is the force between the two particles a and b, qa and qb are the charges on particles a and b, r is the distance between a and g p ,b, and k is the Coulomb’s constant 8.99x109 (Nm2/C2).

If you have more than two charged particles the force on one would be the sum of the forces acting on it due to the other two

i l b i l di h f h h h hparticles, but not including the forces the other two have on each other.

T t l F ti l C F C d t A F C d t BTotal Force on particle C = Force on C due to A + Force on C due to BFc = Fca + Fcb


Electric FieldElectric FieldThe electric force is a field force it applies force withoutThe electric force is a field force, it applies force without touching (like the gravitational force)

In the region around a charged object, an Electric Field is said to existis said to exist


Electric FieldElectric Field

l f i l i i ld iRules for Drawing Electric Field Lines1. The lines must originate on a positive charge (or

infinity) and end on a negative charge (or infinity).

2. The number of lines drawn leaving a positive charge or approaching a negative charge is

ti l t th it d f th hproportional to the magnitude of the charge.3. No two field lines can cross each other.4. The line must be perpendicular to the surface of

the charge



l i fi ldElectric field• Space surrounding an electric charge (an energetic aura)

• Describes electric force• Around a charged particle obeys inverse‐square law• Force per unit chargep g


Electric field direction• Same direction as the force on a positive chargep g• Opposite direction to the force on an electron







F

EFE

becomes 2cqE k

0q 2c r

• E electric field strength, N/C VECTOR• q + test charge C• q0 + test charge, C• q charge producing field, C• r distance between charges m• r distance between charges, m• FE Electric Force, N VECTOR• k coulomb constant 8 99x109Nm2/C2


• kc coulomb constant, 8.99x10 Nm /C

E Field vs g fieldE‐Field vs g‐field

FieldE fieldgFieldE

fieldg

0FE

Fg g

0qE

0mg

0q 0

Coulomb’s LawCoulomb s Law

Differences between gravitational and electrical forces• Electrical forces may be either attractive or repulsive.• Gravitational forces are only attractive.y


E FieldE‐Field

qE ˆ1rqE ˆ

4 2r4 2

0

Electric PotentialElectric Potential

Electric potential energy• Energy possessed by a charged particle due to its gy p y g plocation in an electric field. Work is required to push a charged particle against the electric field of a g p gcharged body.



(a) The spring has more elastic PE when compressed. (b) The

small charge similarly has more PE when pushed closer to the charged sphere. In both cases, the increased PE is the result ofthe increased PE is the result of

work input.


Electric potential (voltage)• Energy per charge possessed by a charged particle gy p g p y g pdue to its location

• May be called voltage—potential energy per chargeMay be called voltage potential energy per charge• In equation form:

electric potential energyElectric potential Electric potential amount of charge

Electric PotentialElectric potential (voltage) (continued)• Unit of measurement: volt, 1 volt

1 coulomb1 joule

Example:• Twice the charge in same location has twice the electric potential energy but the same electric potential.

• 3 times the charge in same location has 3 times the electric potential energy but the same electric potential (2 E/2 q = 3 E/3 q = V)energy but the same electric potential (2 E/2 q 3 E/3 q V)

Electric Potential

Electric potential (voltage) (continued)Electric potential (voltage) (continued)• High voltage can occur at low electric potential energy for a small amount of chargefor a small amount of charge.

• High voltage at high electric potential energy occurs for lots of chargelots of charge.


Electric Energy Storage• Electrical energy can be stored in a common device called a capacitorcommon device called a capacitor.

• The simplest capacitor is a pair of d ti l t t d bconducting plates separated by a

small distance, but not touching h theach other.

• When the plates are connected to a charging device, such as the battery, electrons are transferred from one plate to the other.


Electric Energy Storage• This occurs as the positive battery terminal pulls electrons from the plate connected to it.p

• These electrons, in effect, are pumped through the battery and through the negative terminal to thebattery and through the negative terminal to the opposite plate.

• The capacitor plates then have equal and opposite• The capacitor plates then have equal and opposite charges:

The positive plate connected to the positive battery terminal– The positive plate connected to the positive battery terminal, and

– The negative plate connected to the negative terminal– The negative plate connected to the negative terminal.


Electric Energy Storage• The charging process is complete when the potential difference between the plates equals the potential p q pdifference between the battery terminals—the battery voltage. g

• The greater the battery voltage, and the larger and closer the plates, the greater the charge that can becloser the plates, the greater the charge that can be stored.

• The energy stored in a capacitor comes from the work• The energy stored in a capacitor comes from the work required to charge it. Di h i h d it b h ki• Discharging a charged capacitor can be a shocking experience if you happen to be the conducting path.


Electric Energy Storage• A common laboratory device for producing high voltages and

creating static electricity is the Van de Graaff generator.


Conductors in Electrostatic EquilibriumConductors in Electrostatic Equilibrium

1 Th l t i fi ld i h i id1. The electric field is zero everywhere inside a conductor.

2 Any excess charge on an isolated conductor resides2. Any excess charge on an isolated conductor resides entirely on the outside surface of the conductor.

3. The electric field just outside the charged3. The electric field just outside the charged conductor is perpendicular to the conductor’s surface.

4. On an irregularly shaped conductor, charge tends to accumulate where the radius of curvature is the smallest i e AT SHARP POINTSsmallest, i.e. AT SHARP POINTS.

Electrostatics: Coulomb’s LawElectric fieldElectric field

1) Imagine a single charged particle. Charged particles around it will either move directly toward it or directly away from it. In thi ill t t ththis way, we illustrate the electric field lines as emanating radially from the charged particlethe charged particle.

2) Imagine a sheet of charged particles: the E‐field will be perpendicular to thebe perpendicular to the surface.

http://www.colorado.edu/physics/PhysicsInitiative/Physics2000.05.98/applets/nforcefield.htmlhttp://www.colorado.edu/physics/PhysicsInitiative/Physics2000.05.98/waves_particles/wavpart3.htmlhttp://www.colorado.edu/physics/2000/waves_particles/wavpart2.htmlhtt // fi i / tilit /d k / l t i fi ld/El t i Fi ld ht

Charged particles and force fields :

Electric fields:


http://www.mrfizzix.com/utilitypage/dukes/electricfield/ElectricField.htmhttp://physics.weber.edu/amiri/director/DCRfiles/Electricity/efiel24s.dcr

Electric fields:

Electrostatics: Coulomb’s Law

Working components of a photocopier

How a photocopier works

Working components of a photocopierPhotoreceptor drum (or belt) Corona wiresLamp and lensesLamp and lensesTonerFuser

A drum is basically a metal roller covered by a layer of photoconductivet i l Thi l i d t f i d t h l i imaterial. This layer is made out of a semiconductor such as selenium, germanium

or silicon. What makes elements like selenium so cool is that they can conduct electricity in some cases, but not in others. In the dark, the photoconductive layer on the drum acts as an insulator resisting the flow of electrons from one atom toon the drum acts as an insulator, resisting the flow of electrons from one atom to another. But when the layer is hit by light, the energy of the photons liberates electrons and allows current to pass through! These newly freed electrons are what neutralizes the positive charge coating the drum to form the latent image


what neutralizes the positive charge coating the drum to form the latent image.




Working components of a photocopierPhotoreceptor drum (or belt)Corona wiresLamp and lensesLamp and lensesTonerFuser

For a photocopier to work, a field of positive charges must be generated th f f b th th d d th Th t kon the surface of both the drum and the copy paper. These tasks are

accomplished by the corona wires. These wires are subjected to a high voltage, which they subsequently transfer to the drum and paper in the form of static electricityelectricity.

One of these wires is stretched parallel to the drum surface and charges the photoconductive surface with positive ions, and the other wire is positioned to coat the paper's surface as the paper shoots by on its way to the drum


coat the paper s surface as the paper shoots by on its way to the drum.




Working components of a photocopierPhotoreceptor drum (or belt)Corona wiresLamp and lensesLamp and lensesTonerFuser

Making a photocopy requires a light source with enough energy to boot electrons out of the semiconductive coating on the drum (also called a photoconductor, is this case). What wavelengths of light can do this? It turns out that most of the visible spectrum of light contains enough energy to drive the process, especially the green and blue end of the spectrum. Anything lower than h d i f h i ibl d ' h h i hthe red portion of the visible spectrum doesn't have enough energy to activate the photoconductor. And, although UV light has more than enough firepower to make a photocopy, it can be very damaging to our eyes and skin. This is why h t i l i ld i d t fl t b lb t fl h li ht t


photocopiers use a plain old incandescent or fluorescent bulb to flash light onto the original document.


Working components of a photocopierPhotoreceptor drum (or belt)


Photoreceptor drum (or belt)Corona wiresLamp and lensesToner

Toner is sometimes referred to as dry ink, but toner isn't actually ink at all!

TonerFuser

Toner is sometimes referred to as dry ink, but toner isn t actually ink at all! Ink is a pigmented liquid. Toner is a fine, negatively charged, plastic‐based powder. The black color in photocopier toner comes from pigments blended into the plastic particles while they are being made. pa c es e ey a e be g ade

Toner is stuck on larger, positively charged beads and stored inside a toner cartridge. When toner‐coated beads are rolled over the drum, the toner particles find the positively charged ions on the unexposed areas on the drum's surface attractive.The same particles are subsequently even more drawn to the electrostatically charged paper. The plastic in the toner lets you keep it from jumping ship once you've finally got it on the paper; all you have to do is apply heat to the toner, and the plastic particles


melt and fuse the pigment to the paper.

Xerography: uses photoconductive material coating(Selenium) a drum


Millikan Oil-Drop Experiment p p

Millikan Oil Drop ExperimentMillikan Oil-Drop Experiment

• Robert Millikan measured e, the charge of the electron e = 1.60 x 10‐19 C

• He also demonstrated the quantized nature of• He also demonstrated the quantized nature of this charge

Oil-Drop ExperimentOil Drop Experiment

• With no electric field between the plates:

The drop reaches terminal velocity with FD = mg

Oil-Drop Experimentp p• When an electric field is set up between the plates the p pdrop moves upwards and reaches a new terminal velocityvelocity

• F = mg +F =qEFe = mg +FD =qE

• Solve for qSolve for q•Observed thousands of times and always found e=multiple of 1.6x10‐19 C

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Electrostatics - folk.uio.nofolk.uio.no/ravi/cutn/elec_mag/3_electrostatics2.pdf · Electrostatics: Coulomb’s Law The INSTRUMENT: The torsion balance P.Ravindran, PHY041: Electricity