In the name of God

Chapter 5 and 6

by

Seyedeh Sedigheh Hashemi

OUTLINE

1. Electrostatics Is Gauss’ Law2. Equilibrium In Electrostatic Field3. Equilibrium With Conductors4. Stability Of Atoms5. The Field Of A Line Charge6. A Sheet Of Charge;2 Sheets7. A Sphere Of Charge ;A Spherical

Shell

2 laws of electrostatics

Gauss ‘law

E is a gradient

Carl Friedrich Gauss(30 April 1777 – 23 February 1855)

Would a positive charge remain there?

There is NO points of stable equilibrium in any electrostatic field.

Exceptright on top of another charge!

If were a position of stable equilibrium for a positive charge , the electric field everywhere in the neighborhood would point

toward .

ButA charge can be in equilibrium if there are mechanical constraints.

conductors

Can a system of charged conductors produce a

field that will have a stable equilibrium point for

a point charge?

The Thompson model of an atom(18 December 1856 – 30 August 1940)

The Rutherford model of an atom

30 August 1871 – 19 October 1937

The experiment!

Thompson’s static model had to be

abandoned. Rutherford and Bohr

then suggested that the

equilibrium might be dynamic ,with

the electrons revolving in orbits.

The field of a line charge

𝐸=𝜆

2𝜋 ∈0𝑟

A sheet of charge ; two sheets

𝐸=𝜎2∈0

2 charged sheets

E(outside ) = 0

Uniformly charged sphere

Is the field of a point charge exactly ?

=1

The validity of Gauss ’ law depends upon the

inverse square law of Coulomb.

How shall we observe the field inside a charged sphere?

Benjamin noticed that the field inside a conducting sphere is 0 !

Benjamin Franklin (January 17, 1706 – April 17, 1790)

The Experiment:

The fields of a conductor

The electric field just outsidethe surface of a conductorIs proportional to the local Surface density of charge.

The field in a cavity of a conductor

Thanks 4 ur

attention

In the name of God

Chapter 6 By

Seyedeh Sedigheh Hashemi

• The Electric Field in various circumstances

May 11, 1918 – February 15, 1988

Chapter 6

Outline

I. Equations of the electrostatic potential II. The electric dipole III. Remarks on vector equations IV. The dipole potential as a gradient V. The dipole approximation for an arbitrary

distribution VI. The fields of charged conductorsVII.The method of images VIII.A point charge near a conducting plane IX. A point charge near a conducting sphere X. Condensers; parallel plates XI. High-voltage breakdown XII.The field emission microscope

Part 1

Equation of the electrostatic potential

The whole mathematical problem is the solution of :

Poisson equation:

𝝓(𝟏)=∫ 𝝆 (𝟐)𝒅𝑽𝟐

𝟒𝝅∈0𝒓𝟏𝟐

Part 2

In an insulator the electrons can not

move very far . they are pulled back

by

the attraction of the nucleus . there is

a tiny separation of its + and –

charges. And it becomes a

microscopic dipole

Water moleculeThe hydrogen atom s have slightly less Than their share of the electron cloud ;The Oxygen ,slightly more.

In dipole potential if “d” is much more than “z”, we can write:

The difference of these 2 terms:

if and p=qd

𝜙(𝑥 , 𝑦 ,𝑧)=1

4𝜋 ∈0

𝑝cos𝜃𝑟2

DIPOLE MOMENT OF 2 CHARGES:

Dipole potential:

We wrote the equations in vector form so that they no

longer depend on any coordinate system.

Part 4

= is the potential of a unit point charge.

Two uniformly charged spheres , superposed with a slight displacement ,

are equivalent to a non uniform distribution of surface charge.

Part 5

the potential from the whole collection is:

for r=R

Q is the total charge of the whole object.

We need a more accurate expression for r

that is a dipole potential

Part 6

Part 7

feels a force toward the plate:

Part 8

𝑞′ ′=−𝑞′=𝑎𝑏𝑞

Part 9

𝜙1−𝜙2=𝑉

𝑉=𝐸𝑑= 𝑑∈0 𝐴

𝑄

𝑄=𝐶𝑉¿

Electric field near the edge of two parallel plates

The electric field near a sharp point on a conductor is very high

Thanks 4 ur

attention