Electrostatics laboratory of the 1700s

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When the electric field is uniform, V = Ed

When the electric field is NOT uniform

V Ed

But for anisolated

concentrationof chargewe have

q/rV k=

+

+

?

A large conducting sphere of radius R initially carries an initial charge.

When touched to a smaller, unchargedconducting sphere of radius r < R

charge flows to the smaller sphere until

1. each sphere carries half the total charge.2. each sphere carries the same density of charge.3. charge is divided between them in proportion to their radii: q/Q = r/R.

Two conducting spheres (radius R and r),after touching, are at the same potential.

R

Qk

r

qk=

=q QR

rR

r

Q

q =or

QR

rq =

But check out a comparison of the charge DENSITY across the surface of each:

24 r

q

π24 R

Q

π

If then 22 4

/

4 r

RrQ

r

q

ππ=

rR

Q

π4=

244 R

Q

rR

Q

ππ>

And how do these compare:1. >2. =3. <

But check out a comparison of the charge DENSITY across the surface of each:

24 r

q

π24 R

Q

π

Although Q > q 24 r

q

π24 R

Q

π

The charge density across the surfaceof the smaller sphere is HIGHER!

Charge is crowded togethermuch more tightly on the smaller sphere!

This charged ellipsoidal conductor

1. has its electric charge uniformly distributed across its surface.2. has denser charge packed across the broad, blunt surface at left.3. has denser charge packed across the small, pointier end at right.

Consider electrons spread out acrossthe surface:

A bump or imperfectionon an otherwise smoothsurface:

A sharp point:

are effectivelyregions withsmall radii

and enormouselectric fields!

If you’ve had any chemistry, you may recall

electron pairs fill sub-orbitals:

Hydrogen has 1 proton, 1 electron

Oxygen has 8 protons, 8 electrons

Two most inner orbitals are “filled.”

Two outer orbitals are only “half-filled.”

Oxygen is more "electronegative" or electron "loving" atom than hydrogen.

(the electron affinities we discussed)

Two hydrogen bind with a single oxygen atom to make H2O.

“Electronegative" oxygen shares

an electron(half-time) with each hydrogen.

The positive charge of the hydrogen’s nucleus is only “half-cancelled”.

On average, the oxygen part of the molecule is left slightly negative.

The result is a slight attractionbetween nearby water molecules

NaCl crystal

The “polar” water molecules are attracted to…cling tothe separated ions, shielding them from one another!

explaining water’s role as a powerful solvent!

Soap and detergents are long chain molecules(animal/vegetable oils/fats or

petrochemical hydrocarbon chains)with one end that ionizes in water.

The ionized end (the one that gets charged)attracts water molecules (which are always

slightly polarized)

“hydrophilic”

The neutral end (ignored by the water molecules that crowd the hydrophilic end) is effectively water-proof. “hydrophobic”

Principles of static electricity explainhow a Xerox copier works:

An array of highvoltage wire tips

spray their coronadischarge across aphoto-conductive,semi-conductingsheet of plastic

a material which conducts electricity

when exposed to light, but behavesas an insulator

when in the dark.

charging up the sheet

uniformly inthe dark.

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The photo-conducting sheet has a metallic backing which is grounded.

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Brightly focused spots of light selectively erases isolated spots of charge.

Electrons are driven off the backing to the ground.

- - - - - - - -

- - - - - - - -

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- - - - - - - -- - - - - - - -

- -- -- -

- -- -- -

projecting image

The toner cartridge carries a mix of dryblack tiny plastic flakes (the toner)

and very tiny teflon-coated ball bearings

generates an invisible charge image on the plastic

carrier ball

base

Applying toner

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paper

Heater

QUESTION 1

Charge will flow between the spheres only until thevoltage between them comes into balance: kQ/R = kq/r.

1.QUESTION 2

QUESTION 3

3. charge is divided: q/Q = r/R.

244 R

Q

rR

Q

ππ>

3. has denser charge packed across the small, pointier end at right.

The only difference between these is a factor of 1/r on the left compared to 1/R on the right (the left hand side is Q/4πR r, the right Q/4πR R. Dividing by a big number always gives a

smaller result!

Charge density is only distributed uniformly across the surfaceof smooth, featureless spheres. Otherwise it concentrates at

tight curves, sharp corners and points.