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Physics 1010:The Physics of Everyday Life

TODAY• Electrostatics• Magnetostatics

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Admin Stuff

• If you need grade verification for yourscholarship, see me after class

• Prof. Finkelstein will give lecture onTuesday (circuits)

• HW 7 is due by midnight Monday• Some HW grades have been mixed up, Jing

is looking into it

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“Kinds” of Forces(forces that we talked about in class)

• spring force• normal force: force perpendicular to a surface• Gravity• Friction• Force due to pressure• Centripidal

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• person’s force (pushing or pulling)• gravity• spring force• normal force: force perpendicular to a surface• friction: force tangent, or parallel, to a surface• fluid pressure (times area)• tension (of a rope)

“Kinds” of Forces(forces that we talked about in class)

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• person’s force (pushing or pulling)• gravity• spring force• normal force: force perpendicular to a surface• friction: force tangent, or parallel, to a surface• fluid pressure (times area)• tension (of a rope)

However: this is not a very insightful or even useful classification offorces; it merely summarizes some of the forces we’ve dealt with.

“Kinds” of Forces(forces that we talked about in class)

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The Four Fundamental Forcesand Unifications Leading Thereto and Therefrom

Gravitational

Electromagnetic

(the) Weak force

(the) Strong force

Electric forceMagnetic force GUT ?

(grandunifiedtheory)

Electroweakinteraction

Theory of Everything ?: BIG GUT = GUT + Gravity,explains all forces as aspects of a singleinteraction theory

} } }Interplanetary

Apples on earth} }today’s subject

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Frictions is

A) GravityB) ElectromagneticC) The Weak ForceD) The Strong Force

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Frictions is

A) GravityB) ElectromagneticC) The Weak ForceD) The Strong Force

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Pulling on a string is

A) GravityB) ElectromagneticC) The Weak ForceD) The Strong Force

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Pulling on a string is

A) GravityB) ElectromagneticC) The Weak ForceD) The Strong Force

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The spring force is

A) GravityB) ElectromagneticC) The Weak ForceD) The Strong Force

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The spring force is

A) GravityB) ElectromagneticC) The Weak ForceD) The Strong Force

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The buoyancy force is

A) GravityB) ElectromagneticC) The Weak ForceD) The Strong Force

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The buoyancy force is

A) GravityB) ElectromagneticC) The Weak ForceD) The Strong Force

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• Except for gravity, all of the “kinds” of forces wedraw in force diagrams are due to theElectromagnetic force (mostly electric)

• friction• tension• fluid pressure• normal force• “pushing” force• spring force

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Lennard-Jones Potential

Force ~ - slope

r

r

V

All “contact” forces(spring force, friction,water pressure, etc)are a result of molecules“pushing” or “pulling”against each other. They are all due to the Lennard-Jones potential.

This force isELECTROSTATIC

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The electric force

Electric charge comes in two “flavors”: it can be positiveor negative. Pick the statement that best characterizesthe “direction” of the electric force:

A. Like charges attract (each other); opposites attractB. Like charges repel; opposite charges attractC. Like charges attract; opposite charges repelD. Like charges repel; opposite charges repel

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The electric force

Electric charge comes in two “flavors”: it can be positiveor negative. Pick the statement that best characterizesthe “direction” of the electric force:

A. Like charges attract (each other); opposites attractB. Like charges repel; opposite charges attractC. Like charges attract; opposite charges repelD. Like charges repel; opposite charges repel

Answer: B. For example, two electrons wouldaccelerate away from each other, and two protonswould accelerate away from other, but an electron anda proton would accelerate toward each other (electronshave negative charge, protons are positive).

+ +

- -

+ -

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Elementary Charge• Animal hair (wool, fur) likes to acquire a positive

charge from (or give up a negative charge to)rubber

• Silk likes to acquire a negative charge from (orgive up a positive charge to) glass

• Where do the charges come from?

All macroscopic charges are integer multiples of the electron(negative) or proton (positive) charge.

Amounts of charge are measured in Coulombs (C).A proton has a charge 1.60 x 10-19 C; an electron has a charge-1.60 x 10-19 C. That is, 6.25 x 1018 protons make 1 C ofcharge; 1 C is a lot of charge.

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Charge Conservation

• Although neither electrons nor protons areconserved (both can be created and destroyed) theTOTAL CHARGE IS ALWAYS CONSERVED.

• Just as energy and momentum conservation allow usto solve otherwise difficult problems, so chargeconservation will allow us to solve some toughproblems.

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Calculating gravitational and electric forces

• Gravitational force between two masses,m1 and m2, separated by distance r:

+ +- -+ -

!

F1on 2,g = Gm1m2

r2m1 m2

rG = 6.67 x 10-11 N m2/kg2

• Electric force between two charges, q1 andq2, separated by distance r:

!

F1on 2,e = kq1q2

r2

q1 q2

r

k = 8.99 x 109 N m2/C2

“Coulomb’s Law”

“Newton’s Law of Gravitation”

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Aside: Inverse-Square LawsBoth the electric and gravitational forces obey inverse-squarelaws:F∝1/r2 -- the force (of one mass or charge on another) isproportional to the inverse square of the distance (betweenthem).

Most important: the force diminishes with distanceSecond most important: doubling the distance quarters theforce

Inverse-square laws reflect the three-dimensionality of ouruniverse: the area of a 3D sphere of radius r is A = 4πr2 ∝ r2 .“Stuff” spreading out in 3 dimensions obeys an inverse-squarelaw.

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Inverse-Square LawsA special spray-paint nozzle spraysequally in all directions. In 1 min., itpaints a 1mm thick coat on the insidesurface of a sphere of radius 1 m.How thick would the paint be if thesphere had a 2 m radius?A. 1/8 mmB. 1/4 mmC. 1/2 mmD. 1 mmE. 2 mm

Area of sphere = 4πr2

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Inverse-Square Laws

B. The 2 m sphere has 4 times the area (A ∝ r2) of the1 m sphere, but receives the same TOTAL amount ofpaint in the same time; therefore, the paint must be 1/4as thick. After 1 min. of spraying, the thickness ofpaint on a sphere of radius r varies as 1/r2 -- an inverse-square law. “Stuff” spreading out in 3 dimensions obeysan inverse-square law (e.g., light and sound intensity).

A special spray-paint nozzle spraysequally in all directions. In 1 min., itpaints a 1mm thick coat on the insidesurface of a sphere of radius 1 m.How thick would the paint be if thesphere had a 2 m radius?A. 1/8 mmB. 1/4 mmC. 1/2 mmD. 1 mmE. 2 mm

Area of sphere = 4πr2

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Calculating gravitational and electric forcesbetween two protons: Clicker Question

• Gravitational:

!

F1on 2,g = Gm1m2

r2 G = 6.67 x 10-11 N m2/kg2

• Electric force:

!

F1on 2,e = kq1q2

r2k = 8.99 x 109 N m2/C2

Each proton (shown left) hasmass m = 1.67 x 10-27 kg andcharge q = 1.60 x 10-19 C.Considering the electric force Fe andgravity Fg, will two protons separatedby r = 1mm be attracted or repelled?

q,m q,m

r=1 mm

!

F1on 2,g

!

F1on 2,e

!

Fe

Fg

=

kqq

r2

Gmm

r2

=kq2

Gm2=(8.99"109Nm2

/C2)(1.60"10#19C)2

(6.67"10#11Nm2/kg2

)(1.67"10#27kg)2=1.24"1036

1 2

What is the ratio of strengths, Fe/Fg ?

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The Electric Force is much, much strongerthan Gravity (comparing protons). Why then,

is gravity so much more noticeable?

A gravity deals with much larger bodies B depends on difference in chargeC gravity does not have a positive and negativeD

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The Electric Force is much, much strongerthan Gravity (comparing protons). Why then,

is gravity so much more noticeable?The attraction between positive and negative chargesis so strong that positive and negative charges tend toclump together, canceling each other out. For example,atoms:

++

++

+ +

-

-

-

-

-

-A carbon atom:A nucleus with 6 protons(and 6 neutrons), with6 electrons.Net charge: zero

Nature abhors a charge imbalance(because net charges produce strong forces on each other)

Note: the Strong Force holds the nucleus together; over very short distances, theStrong Force is stronger than the electric force.

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Charge “clumping” reduces electric force

A positive and negative charge close togetherconstitute an electric “dipole”; single charges are“monopoles”.Dipoles do not obey the inverse square law; theforce a dipole exerts on a charge (or on anotherdipole) falls off with distance much faster than1/r2

This will be important in magnetostatics, becausethere are no magnetic “monopoles”; only dipoles.

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An insulator does not allow charges to movewithin it; in an insulator, charges cannot move.

+-+

An insulator (above, right) has equal and opposite chargesplaced on each end. A positive charge (above, left) isplaced at a large distance from the insulator:

A. The insulator will be attracted to the charge.B. The insulator will be repelled by the charge.C. Neither of the above

Dipole forces fall off much faster than 1/r2

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+-

+

An insulator (above, right) has equal and opposite chargesplaced on each end. A positive charge (above, left) isplaced at a large distance from the insulator:

A. The insulator will be attracted to the charge.B. The insulator will be repelled by the charge.C. Neither of the above

Answer: C. Because the charge on the left is far from the dipole,forces of the external charge on the positive and negative partsof the insulator are almost equal and opposite.

Dipole forces fall off much faster than 1/r2

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What does “far away” mean?How far away do you have to be for the

force to be negligible?

• A inverse square• B REALLY far• C much farther than the size of the dipole• D

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+-

+

An insulator (above, right) has equal and opposite chargesplaced on each end. A positive charge (above, left) isplaced at a large distance from the insulator:

A. The insulator will be attracted to the charge.B. The insulator will be repelled by the charge.C. Neither of the above

Answer: C. Because the charge on the left is far from the dipoleCOMPARED TO THE SIZE OF THE DIPOLE, forces of theexternal charge on the positive and negative parts of the insulatorare almost equal and opposite.

Dipole forces fall off much faster than 1/r2

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Clicker QuestionA conductor allows charges to move freelywithin it; in a conductor, charges move freely.

+-+

Suppose a conductor has two equal and opposite charges;they can move freely, so they attract each other untilthey’re almost in the same place.When a positive charge is brought close to the conductorfrom the left:

A. The conductor will be attracted to the charge.B. The conductor will be repelled by the charge.C. Neither of the above

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Clicker QuestionA conductor allows charges to move freelywithin it; in a conductor, charges move freely.

+-+

Suppose a conductor has two equal and opposite charges;they can move freely, so they attract each other untilthey’re almost in the same place. When a positive chargeis brought close to the conductor from the left:A. The conductor will be attracted to the charge.B. The conductor will be repelled by the charge.C. Neither of the above

Answer: A. Because the conductor has zero net charge, the net force on it will be small;however, since the charges are free to move within the conductor, the positive charge willbe repelled slightly, while the negative charge will be attracted. Since the distancebetween the negative charge and the external charge is less than that between the positivecharge and the external charge, the negative charge is attracted more strongly than thepositive charge is repulsed (c.f. Coulomb’s Law). Therefore, the conductor experiences anet force toward the left.

+-+The external charge“polarizes” the conductor:

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Magnetic poles are like electric charges• If they are close together,

the two magnets to theright will

a) Attractb) Repelc) Have no effect on each

other

N

S

N

S

The correct answer is (b), like poles repel each other,and the two south poles are closest, so their forcesare the most important

Magnetostatics

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Many similarities with electric forces• Like poles repel• Opposite poles attract• Force grows weaker at greater

distances• Some choice of sign: + pole =

north pole = pole that seeksthe north

N

S

Exception: magnetic poles always come in pairs!Cut a magnet, get two magnets, each with anorth and south pole.THERE IS NO MAGNETIC MONOPOLE

N

S

NS

NS

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The earth is one big magnet

Is the north pole of the earth a magnetica) North poleb) South polec) Neither

The correct answer is (b), north poles of magnets areattracted to the north of the earth, so the north pole ofthe earth is the south pole of the magnet earth.

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Magnetic poles are like electric charges

• There is no magnetic “monopole”. All magnetscome with both poles.

• Forces between magnets are therefore verysmall, unless magnets are “close” together

HOWEVER:

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What do we mean by “close”?How close do magnets have to be for the

magnetic force to be significant.

• A REALLY close• B closer than 1/r2

• C as close as the magnet is big• D

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At large distances, magnetic forcesdecrease more rapidly than inverse square

• On left: Upper north polereally close to lower southpole. Feels only that force.

• On right: Upper north poleand upper south pole aboutsame distance from lowersouth pole, so 1/r2 forcescancel, force less than 1/r2

S

N

S

N

S

N

S

NTHAT’S BECAUSE MAGNETIC POLES ALWAYS COME IN PAIRS

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Magnetic materials: poles “move” byattractive force (like charges in conductors)

• Iron, nickle,cobalt, otherelements (rare-earth ceramics)

• Extends themagnet

Neutral bar

S

NS

NN SN S

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Why are some magnets made in the shapeof a horseshoe?

a) Because that shape isknown to give good luck

b) Gives extra pickup powerbecause poles move aroundin the item to pick up

c) Bringing the poles of thehorseshoe togetherintensifies the magneticfield

N S

b) The north pole attractsthe south poles in themedium, but it also helpsrepel more north poles tothe other end where theyare attracted by the southpole of the horseshoemagnet

S N

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Currents produce magnetic fields indirection per right-hand rule

• Wrap fingersaround in directionof coil current

• Your thumb is thenorth pole

Current

North pole

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Permanent magnets: the spinningelectrons line up

• Electrons have negativecharge, so opposite ofright-hand rule

• Ferromagnetic material:spinning electrons lineup

• Non magnetic material:other forces preventalignment

N N

N N

N

NNN

N

N

N

N

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The earth has a magnetic south pole at itsgeographic north pole

The currents flowing insidethe earth flow

a) from west to eastb) from east to westc) from north to southd) from south to north

N

(b) From east to west so that the right handrule gives the thumb going out the south pole

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Motors can use permanent magnets andelectromagnets

• Linear motor• Turn on attraction in

front• Turn on repulsion behind• After moves, change

coils to keep going• Usual motor: put into

circle

SN

N

N

S

S

SN

N

N

S

S

SN

N

N

S

S

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Electromagnetic induction - movingmagnets (or changing magnetic fields)cause currents to flow, magnetization

• Moving electric charges causemagnetic fields (Oersted,Ampere, 1820)

• Moving magnetic poles causeelectric fields (Faraday, 1831)= Induction

Rising current, counterclockwise from top

Metal block

Causes current in metalthat is clockwise from top

Induction is how we produce allour electricity (except batteries)

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Lenz’s law: Current induced by a changingmagnetic field always produces a magnetic

field that opposes the change

• Produces oppositecurrent

• Opposite magneticfields

• NOT magnetization

Current North pole

SN

Current North pole

Induced current Induced north pole

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Summary

• Electric and magnetic forces similar• Electric charge comes in monopoles,

magnetic poles only in dipoles• Currents produce magnetic fields• Changing magnetic fields produce currents