electrical forces,magnetic forces,

action-at-a-distanceFields

Mico-world Macro-world

Lecture 8

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Benjamin Franklin

Ben FranklinMatter is filled with a mysteriousFluid-like substance called “electricity.”

When an object has its “normal amount”of electricity, it is electrically “neutral”And doesn’t feel electrical forces.

When an object has more than its normalamount of electricity, it is “positively charged.” When it has less than its normal amount it is “negatively charged.”

Charged objects feel electrical forces.

Friction can move “electricity” from one object to another

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Franklin hypothesized that rubbing a comb through hairmoved some “electricity” from the comb to the hair

Comb has an “electricity”deficit & thus becomesnegatively charged

Hair has a surplus& becomespositively charged

Opposite charges attract

Like-sign charges repel

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Modern picture of “electricity”

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Negatively charged electronsorbit around a positively charged nucleus

Electrical attractionbetween minus electrons & plus nucleus keeps electrons in orbit

Positive Ion

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An atom with one or moreelectrons removed

”net” charge is positive

“electricity” flow

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Comb has an excess ofof electrons & is thusnegatively charged

The removal ofeach electron leaves a positive ions in the hair

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“electricity” doesn’t flow from comb to hair, someelectrons from hair atoms get stuck on the comb

Atomic electrons play the role of“fluid-like electricity”

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ElectricalConductors

+ + + + + ++ + +

+ + + + + ++ + ++ + + + + ++ + +

+ + + + + ++ + ++ + + + + ++ + +

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+positive ion(fixed in crystal)

_ Conduction electronfree to move around

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Charging by induction

Charging by induction (2)

Electroscope

Electrical Force

Charles Coulomb 1736-1806

Coulomb’s Law

The electrical force between two charged objects is proportional to the charge of each object and inversely proportional to the square of the distance between them.

Coulomb’s law

q1 q2r

Fc q1

Fc q2

Fc 1r2

combine: Fc q1q2

r2 Fc = kq1q2

r2

Proportionality constant:

“Coulomb’s Constant”

proportional to thecharge of each object

Inversely proportional to the square of the distance between them

Units & Coulomb’s constant

Fc = kq1q2

r2

Unit of charge = “Coulomb”(C)

Unit of distance = m

k = 9.0 x 109 Nm2/C2

This is a big number

Hydrogen atom

qe = -1.6x10 –19 Celectron

proton

qp = +1.6x10 –19 C

Fc = kqeqp

r2

=9x109Nm2/C2(1.6x10-19C)2

(5x10-11m)2

=9.2x10-8N

5x10–11 m

Gravitational force in an atom

me = 9.1x10 –31 kg

electron

proton

mp = 1.7x10 –27 kg

FN = Gmemp

r2

9.1x10-31kgx1.7x10-27kg(5x10-11m)2

=4.1x10-47N

5x10–11 m

=6.7x10-11Nm2/kg2

Electrical vs gravitation at atomic scales

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5x10–11 m FN=4.1x10-47N

FC=9.2x10-8N

FC 9.2x10-8N

FN 4.1x10-47N= = 2.2x10+39

Electrical force is >1039x the gravitational force!!Fc = 22,000,000,000,000,000,000,000,000,000,000,000,000,000 x FN

Magnetismanother “invisible” force

N-poles & S-poles

NS

NS

Unlike poles attract

N-poles & S-poles

NS

SN

like poles repel

N-poles & S-poles can never be isolated

NS

NS NS

Break a magnet into two pieces:

A new N-pole & S-pole are formed

Compass needles

If left to its own accord, the N-pole of amagnet will try to point towards the North

The Earth is a magnet

SouthPole

NorthPole

N

S

Earth’s geographicNorth pole is a

Magnetic S-pole

geographicSouth pole is a

magnetic N-pole

Action at a Distance

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Coulomb’s law

q1

M1

q2

M2r

Fc = kq1q2

r2

FN = GM1M2

r2

Newton’s law of Gravitation

All possible

distances!

Moon-earth

FN=GMMME

r2

How does the Moonknow that the Earth

is where it is (& what ME is)?

Electroscope

How do the electronsin the foil know thatsomeone is moving a charged object up here?

& that it’s negativelycharged?

& how much it ischarged by?

Ball on an empty trampoline surface

The ball feelsno net force

Ball on a “loaded” trampoline surface

The ball is “attracted” to the girl’s force

Luminiferous aether & E-Fields

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Faraday’s method for computingE fields

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Imaginary small positive “test” charge qtest

Ftest=coulomb force on test charge

Ftest

E = Ftest/qtestx+

Example

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E-field from 2 plus charges

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E-field from 2 plus charges

E-Field is the dir of force on + charge

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E-Field for opposite charges

Better picture

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RulesE-field lines start on + charges and end on - charges

Direction of E-field lines = direction of force on a + charge placed at that point (opposite for – charge)Where E-field lines are close together, the E field is large; where they are far apart, the E-field is small.

The bigger the charge, the more E-field lines start (or stop) on it.

E-field lines never cross

Magnetic Fields

NS

xImagine a smallN-pole is placedat the point

NDetermine themagnetic forceon the imaginaryN-pole

B-field is inthe directionof the netforce

B-field from a bar magnet

NS

Rules

NS

B-field lines come out of N-poles & go into S-poles

B-field lines never end

Density of B-field strength of the field

The stronger the pole, the more B-field exit (or enter)

Arrays of magnets

,arrays of magnets

Earth’s magnetic field

Which ones are N? Which are S?

E-field? or B-field?

1. Which is +?

2. Which is -?

3. Which is bigger?

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Gravitational Fields

mg =

Fm

m

Fmg Rules:

•g-field lines start at infinity & end on mass

•The more dense the lines, the stronger the g-field

•The bigger the mass, the more g-field lines end on it

•At any point in space, g is the acceleration due to gravity there. (On the surface of the earth, g = 10 m/s2.)

test particle force on test particle

mass of test particle

E-field RulesE-field lines start on + charges and end on - charges

Direction of E-field lines = direction of force on a + charge placed at that point (opposite for – charge)

Where E-field lines are close together, the E field is large; where they are far apart, the E-field is small.The bigger the charge, the more E-field lines start (or stop) on it.

E-field lines never cross

B-fieldRules

NS

B-field lines come out of N-poles & go into S-poles

B-field lines never end

Density of B-field strength of the field

The stronger the pole, the more B-field exit (or enter)