Interaction of Charged Objects

Attraction: can happen also for like-charged objects!

Repulsion: can happen only for like-charged objects!

Intervening matter does not “block” the E field

The resulting field is a superposition of two fields: Field of the charge plus the field of induced dipoles.

+ - +

Clicker QuestionA

B D

C

What is the direction of the electric field at X due to the dipole?

Clicker QuestionA

B D

C

What is the direction of the electric field at X due to the plastic block?

Clicker QuestionA

B D

C

What is the direction of the NET electric field at X?

Clicker Question

The force of one of the permanent dipoles on the other is:

A) AttractiveB) RepulsiveC) The force is zero

Different materials respond differently to electric field

Conductor: contains mobile charges that can move through material

Insulator: contains no mobile charges

Conductors and Insulators

Insulator: Electrons are bound to the atoms or molecules.

Electrons can shift slightly (<1 Å), but remain bound to the molecule.

Individual atoms or molecules can be polarized by external electric field.

There are a lot of molecules – the net effect produced by the induced dipoles can be very large.

Polarization of Insulators

Diagram showing polarization of an insulator:

Dipoles: exaggerated in size; stretch: degree of polarization

No mobile charges: excess charges stay where they are

Polarization of Insulators

Field E at a location of a molecule is a superposition of the external applied field and the field created by other induced dipoles:

Simplifying assumption:

Low Density Approximation

There are charges which can move freely throughout the material

E

In contrast to an insulator, where electrons and nuclei can move only very small distances, the charged particles in a conductor are free to move large distances.Polarization of conductors differs from that of insulators.

Conductors

Salt water:Na+ and Cl-

H+ and OH-

Apply externalelectric field

Ionic Solutions are Conductors

When an electric field is applied to a conductor, the mobile charged particles begin to move in the direction of the force exerted on them by the field.

As the charges move, they begin to pile up in one location, creating a concentration of charge creates electric field.

The net electric field is the superposition of the applied field and field created by the relocated charges.

Assumption: charges will move until Enet=0 (static equilibrium)

It is not a shielding effect, but a consequence of superposition!

Proof: by contradiction:

Mobile ions will move

This is not equilibrium

Assume Enet≠0

Assumption Enet≠0 is wrong

Enet=0

Ionic Solutions are Conductors

Positive atomic coresand mobile-electron sea

Electrons are not completely free – they are bound to the metal as a whole.

Metal lattice

There is no net interaction between mobile electrons

A Model of a Metal

We will return to this idea when we discuss the force on a current carrying wire in a magnetic field.

Simplified diagram of polarized metal

Note: It is not charged!Net charge is still zero

Metal in Electric Field

In static equilibrium:

Enet= 0 everywhere inside the metal!

Mobile charges on surface rearrange to achieve Enet= 0 Actual arrangement might be very complex!

It is a consequence of 1/r2 distance dependence

Enet= 0 only in static equilibrium!

Electric Field inside Metal

E

-

• No net interaction between mobile electrons

• Forget previous velocity after collision conductivity () μ

Collisions:- impurities- thermal motion of atoms

Higher temperature T shorter lower

Drude Model of Electron Motion in a Metal

∆𝑝∆ 𝑡

=𝐹 𝑛𝑒𝑡=(−𝑒)𝐸𝑛𝑒𝑡

∆ 𝑝=𝑝− 0=(−𝑒)𝐸𝑛𝑒𝑡 ∆ 𝑡

𝑣=𝑝 /𝑚𝑒=−𝑒𝐸𝑛𝑒𝑡∆ 𝑡  

𝑚𝑒

𝑣=𝑒∆ 𝑡𝑚𝑒

𝐸𝑛𝑒𝑡𝜇=𝑒∆𝑡𝑚𝑒

;𝑚𝑜𝑏𝑖𝑙𝑖𝑡𝑦

Excess charges in any conductor are always found on an inner or outer surface!

Excess Charge on Conductors

Conductor Insulator

Mobile charges yes no

Polarizationentire sea of mobile charges

movesindividual atoms/molecules

polarize

Static equilibrium

Enet= 0 inside Enet nonzero inside

Excess charges only on surfaceanywhere on or inside

material

Distribution of excess charges

Spread over entire surface located in patches

Conductors versus Insulators

Discharging by contact:

On approach: body polarizes

On contact:charge redistributes over larger surface

Grounding: connection to earth (ground) – very large object

Charging and Discharging

Charging by Induction

Charging by Induction

An object can be both charged and polarized

On a negatively charged metal ball excess charge is spread uniformly all over the surface.

What happens if a positive charge is brought near?

+

Exercise

Splitting universe into two parts does not always work.

+q

If q is so small that it does not appreciably alter the charge distribution on the sphere, then we can still use the original field:

Otherwise, we must calculate new field:

When the Field Concept is less Useful