II. Electric Field[Physics 2702]

Dr. Bill Pezzaglia

Updated 2015Feb09

II. Electric Field

A. Faraday Lines of Force

B. Electric Field

C. Gauss’ Law (very lightly)

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A. Lines of Force

1) Action at a Distance

2) Faraday’s Lines of Force

3) Principle of “Locality”

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1. “Action at a Distance”

• Newton proposes gravity must act instantaneously, regardless of distance (else angular momentum not conserved).

• “actio in distans” (action at a distance), no mechanism proposed to transmit gravity

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"...that one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that, I believe no man, who has in philosophic matters a competent faculty of thinking, could ever fall into it." -Newton

Sir Isaac Newton(1643-1727)

How does moon “know”the earth is there to falltowards it?

2a. Sir Humphry Davy 1778 - 1829

•1807 Electrolysis, used to separate salts. Founds science of electrochemistry.

•His greatest discovery was Michael Faraday.

•1813-15 takes Faraday with him on grand tour visiting Ampere and Volta.

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2b. Michael Faraday 1791 - 1867

•1821 First proposes ideas of “Lines of Force”• Example: iron filings over a magnetic show field lines

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2c. Electric Lines of Force

•Electric charges create “electric field lines”•Field lines start on + charges, end on –•A plus charge will tend to move along these lines

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2d. Other Properties •Field Lines can’t cross (else physics would not be deterministic, ambiguity which way to go)

•Density of lines is proportional to the “strength” of the force

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3. Principle of Locality

• Argues that the field lines have independent reality

•Force fields exist as distortions in the “aether” of space

•Alternative to “action at a distance”, charges Locally interact with force lines

•Ideas rejected by others. He can’t put them into mathematical form.

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I cannot conceive curved lines of force without the conditions of a physical existence in that intermediate space. (Michael Faraday)

B. Electric Field

1) Definition of Field

2) Sources of Field

3) Electrodynamics

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1a. James Maxwell (1831-1879)

•1855 essay On Faraday's Lines of Force, suggests lines are like an imaginary incompressible fluid (obeying hydrodynamic equations)

•1861 paper On Physical Lines of Force, proposes “real” physical model of vortices for magnetic field

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•Definition: force per unit test charge(i.e. don’t want test charge to affect field)

•Units of Newton/Coul (or Volts/meter)

•So force on charge is: F=qE

1b. Definition of Field 13

q

FLimEq

0

+E

Fq

1c. Analogy to Gravity

• Gravitational Force Field:force per unit test mass

• i.e. its an “acceleration of gravity” field

• Mass is the “charge” of gravity: F = mg

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m

FLimgm

0

2. Sources of E Field

(a)Point Charge Source (monopoles

(b)Dipoles

(c) Field of Dipole (incomplete)

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2.a Monopole Sources

• A positive charge is a “source” of electric field. Field radiates outward from a point source

• A negative charge is a “sink” of electric field. Field radiates inward

• Field strength: E=kQ/r2

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2.b Dipole Sources• An “electric dipole” is a “stick”

of length “L” with + charge on one end and equal – charge on other.

• Dipole moment: p=QL• The vector “p” points along axis

from – to + charge

• Units (SI) is Cm• Standard in Chemistry is the

Debye: 1D=3.33564x10-30 Cm

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2.c Field of Dipole

• Derivation will be done on board. Basically you use “superposition” of fields of two monopoles.

• Field of dipole along its axis drops off like the cube of the distance!

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32212

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2)(z

pk

Lz

kQ

Lz

kQzE

3. Electrodynamics

a) Force on monopole

b) Torques on Dipoles

c) Van der Waal Forces

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B.3.a: Force on a Charge (monopole)

• Force on positive charge is in direction of field

• Force on negative charge is opposite direction of field

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EqF

+E

Fq

-E

Fq

B.3.a Point Charge Electrodynamics

• Force between monopoles is hence Coulomb’s law

• Force between dipole “p” and monopole “q” decreases cubically:

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3

2

z

kpqEqF

rR

QqkEqF ˆ

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B.3.b Torque on Dipole

• An electric dipole will want to twist and line up with the electric field

• Torque on a dipole in an electric field is:

• Recall dipole momentp=qL

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cospE

Ep

B.3.c Gradient Forces on Dipole(Van-der-Waal’s forces between molecules,

e.g. Hydrogen Bonding in water)

• If field is not constant (has a “gradient”) then there will be a force on a dipole

• Forces between dipoles (along a line) can be shown to be:

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x

EpLxqELxqEF

)2/()2/(

4216

z

ppkF

C. Gauss’s Law (Lightly)

Ignoring the mathematics, Gauss’s law (1813) has the following results:

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Spherical Symmetry:

Electric field of a spherical ball of charge the same as a point charge:

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Note that the result is INDEPENDENT of radius of ball!

Where “r” is measured from center of ball.

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)(r

QrE

Field is zero inside a conductor

Consider a solid conducting sphere.

Electric charge will be pushed to surface

Electric field inside conductor is zero

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Electric Field inside a conductor is ZERO

Example of Faraday Cage: An external electrical field causes the charges to rearrange which cancels the field inside.

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Cylindrical Symmetry:

Electric field of a charge “Q” spread out on a long cylinder (length “L”) is:spherical ball of charge the same as a point charge:

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Note that the result is INDEPENDENT of radius of cylinder.

e.g. a line charge, or charge on a wire

Lr

QrE

02)(

c. Plane Geometry

Consider a large flat sheet (area “A”) with charge “Q” spread out uniformly. The electric field outside is constant [Laplace 1813].

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A

Q

AE

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With the application of superposition principle, you can show that parallel plates of opposite charge have a constant field between (and zero outside).

A

Q

AE

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References

•http://maxwell.byu.edu/~spencerr/phys442/node4.html

•http://en.wikipedia.org/wiki/Timeline_of_Fundamental_Physics_Discoveries

•http://www.oneillselectronicmuseum.com/index.html

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