Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html

Lecture 5

Chapter 27

Conductors in Electrostatic Equilibrium

02.03.2015Physics II

95.144

Channel 61 (clicker)

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

Electric field inside a conductorConsider a conductor and apply an external electric field.

Conductor has tons of free electrons and under the influence of Eext they will run to the left surface leaving positive charges near the right surface and creating Einternal.

How many of them will move?-The electrons will keep moving until the internal field cancels out the external field inside the conductor

ConductorEext

Eint

Thus, the electric field inside a conductor is zero in electrostatic situation

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

Charges in a conductor

Φ ∙

Consider a positively charged conductorWhere does this excess charge reside in

in the conductor?

Take a Gauss. surface just barely inside the surface of a conductor

Let’s apply Gauss’s law

So Qin =0 (inside the Gaussian surface)

Thus, the positive excess charge resides on the external surface of the conductor

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

E (outside) is ┴ to the surface of a conductor

If it were to have a tangential component, it would exert a force on the surface charges and cause a surface current, and the conductor would not be in electrostatic equilibrium (Proof by contradiction).

The external electric field right at the surface of a conductor must be

perpendicular to that surface.

E

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

E near any conducting surface

A point charge q is located distance r from the center of a neutral metal sphere. The electric field at the center of the sphere is:

ConcepTest 1 ConductorsChannel 61

A)

B)

C)

D) 0E) It depends on what the metal is.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

Charged conductor with a hole inside

Are there any charges on an interior surface?

No charges

Conductor Place a Gaussian surface around the hole.Let’s apply Gauss’s law

Φ ∙

So Qin =0 (inside the Gaussian surface), i.ethere is no charge on the surface of the hole

The electric flux is zero through the Gaussian surface, since E=0 inside the conductor.

0

Any excess charge resides on the exterior surface of a conductor, not on any interior surfaces

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

Screening/Faraday cage I

The use of a conducting box, or Faraday cage, to exclude electric fields from a region of space is called screening.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

Screening/Faraday cage II

• conductive fabrics• metallic inner shields• Vacuum metallization• Conductive paints

Shielding essentially prevents electromagnetic pulses from interfering with the proper functioning of electronics.

A Faraday cage protects its contents by preventing electromagnetic energy from getting inside.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

Let’s put a charge inside the hole

Are there any charges on an interior surface?

Negative charge -q

Conductor

Place a Gaussian surface around the hole.Let’s apply Gauss’s law

Φ ∙

So Qin =0 (the net charge inside the Gaussian surface

The electric flux is zero through the Gaussian surface, since E=0 inside the conductor.

0

Let’s ask the same question again:

Charged (+Q) conductor

But, we know that there is +q inside, it means that there must be –q on the interior surface (+q charge induced –q on the surface)

Let’s count all charges inside the conductor to find the amount of charge on the exterior surface

Q+q

Inner surface The conductor is charged to +Q

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

Conductor with two cavitiesAn uncharged conducting sphere of radius Rcontains two spherical cavities. Point charge Q1is placed within the first cavity (not necessarily atthe center) and Q2 is placed within the secondone. Find the charge on the outer surface.

Charge 3 nC is in a hollow cavity inside a large chunk of metal that is electrically neutral. The total charge on the exterior surface of the metal is

ConcepTest 2 ConductorsChannel 61

A) 0 nC.B) +3 nC.C) –3 nCD) Can’t say without knowing the shape and location of the hollow cavity

+3 nC

-3 nC

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

What you should read

Chapter 27 (Knight)

Sections 27.6 (Conductors in electrostatic equilibrium)

Skip (Example 27.8)

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

E field inside of a charged dielectric sphere

A total charge Q is spread uniformly throughout a dielectric

sphere of radius R. What is the electric field inside the

sphere (r<R)?

ELet’s plot it

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 5

Thank youSee you on Friday