electrical forces, magnetic forces, action-at-a-distance Fields Mico-world Macro-world Lecture 8 + -

Benjamin Franklin

Ben Franklin Matter is filled with a mysterious Fluid-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 normal amount 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 _ _ _ _ Franklin hypothesized that rubbing a comb through hair moved some “electricity” from the comb to the hair Comb has an “electricity” deficit & thus becomes negatively charged Hair has a surplus & becomes positively charged

Opposite charges attract

Like-sign charges repel __

Modern picture of “electricity” _ _ _ _ _ _ Negatively charged electrons orbit around a positively charged nucleus Electrical attraction between minus electrons & plus nucleus keeps electrons in orbit

Positive Ion _ _ _ _ _ _ An atom with one or more electrons removed ”net” charge is positive

“electricity” flow _ _ _ _ Comb has an excess of of electrons & is thus negatively charged The removal of each electron leaves a positive ions in the hair “electricity” doesn’t flow from comb to hair, some electrons from hair atoms get stuck on the comb

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

Electrical Conductors ____ _ _ __ _ _ __ _ _ __ __ __ ____ _ _ __ ____ _ _ __ _ _ _ _ __ _ _ + positive ion (fixed in crystal) _ Conduction electron free to move around _

Charging by induction

Charging by induction (2)

Electroscope

Electrical Force Charles Coulomb

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 q1q1 q2q2 r F c  q 1 F c  q 2 Fc Fc  1r21r2 combine:Fc Fc  q1q2r2q1q2r2 F c = k q1q2r2q1q2r2 Proportionality constant: “Coulomb’s Constant” proportional to the charge of each object Inversely proportional to the square of the distance between them

Units & Coulomb’s constant F c = k q1q2r2q1q2r2 Unit of charge = “Coulomb”(C) Unit of distance = m k = 9.0 x 10 9 Nm 2 /C 2 This is a big number

Hydrogen atom q e = -1.6x10 –19 C electron proton q p = +1.6x10 –19 C F c = k qeqpr2qeqpr2 = 9x10 9 Nm 2 /C 2 (1.6x C) 2 (5x m) 2 = 9.2x10 -8 N 5x10 –11 m

Gravitational force in an atom m e = 9.1x10 –31 kg electron proton m p = 1.7x10 –27 kg F N = G mempr2mempr2 9.1x kgx1.7x kg (5x m) 2 = 4.1x N 5x10 –11 m = 6.7x Nm 2 /kg 2

Electrical vs gravitation at atomic scales + _ 5x10 –11 m F N = 4.1x N F C = 9.2x10 -8 N F C 9.2x10 -8 N F N 4.1x N = = 2.2x Electrical force is >10 39 x the gravitational force!! F c = 22,000,000,000,000,000,000,000,000,000,000,000,000,000 x F N

Magnetism another “invisible” force

N-poles & S-poles NS N S Unlike poles attract

N-poles & S-poles NS S N like poles repel

N-poles & S-poles can never be isolated NS NSNS 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 a magnet will try to point towards the North

The Earth is a magnet South Pole North Pole N S Earth’s geographic North pole is a Magnetic S-pole geographic South pole is a magnetic N-pole

Action at a Distance + -

Coulomb’s law q1q1 M1M1 q2q2 M2M2 r F c = k q1q2r2q1q2r2 F N = G M1M2r2M1M2r2 Newton’s law of Gravitation All possible distances!

Moon-earth F N =G M M M E r 2 How does the Moon know that the Earth is where it is (& what M E is)?

Electroscope How do the electrons in the foil know that someone is moving a charged object up here? & that it’s negatively charged? & how much it is charged by?

Ball on an empty trampoline surface The ball feels no net force

Ball on a “loaded” trampoline surface The ball is “attracted” to the girl’s force

Luminiferous aether & E-Fields +

Faraday’s method for computing E fields + Imaginary small positive “test” charge q test F test =coulomb force on test charge F test E = F test /q test x +

Example ++

E-field from 2 plus charges ++

E-Field is the dir of force on + charge + -

E-Field for opposite charges

Better picture + -

Rules E-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 N S x Imagine a small N-pole is placed at the point N Determine the magnetic force on the imaginary N-pole B-field is in the direction of the net force

B-field from a bar magnet NS

Rules N S 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? _ +

Gravitational Fields m g = FmmFmm FmFm g 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/s 2.) test particle force on test particle mass of test particle

E-field Rules E-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-field Rules N S 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)