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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