PHYS117B: Lecture 6 Electric field in planar geometry. Electric potential energy. - PowerPoint PPT Presentation

About This Presentation
Title:

PHYS117B: Lecture 6 Electric field in planar geometry. Electric potential energy.

Description:

Used Gauss's law to find the field in and out of spheres (conductors and ... in a light weight metal mesh (Faraday cage) to screen any stray electric fields ... – PowerPoint PPT presentation

Number of Views:45
Avg rating:3.0/5.0
Slides: 16
Provided by: hepVand
Category:

less

Transcript and Presenter's Notes

Title: PHYS117B: Lecture 6 Electric field in planar geometry. Electric potential energy.


1
PHYS117B Lecture 6Electric field in planar
geometry. Electric potential energy.
  • Last lecture
  • Properties of conductors and insulators in
    electrostatic equilibrium
  • E 0 inside the conductor and all excess charges
    are on the surface
  • Used Gausss law to find the field in and out of
    spheres (conductors and insulators) and
    similarly we can do spherical shells and spheres
    inside spherical shells
  • The electric field outside a sphere is to the E
    of a point charge located in the center
  • We played with cylinders the previous time

2
The electric field of an infinite charged plane
  • Use symmetry
  • The field is - to the surface
  • Direction away from positive charge, and toward
    a negative charge
  • Use Gausss law to determine the magnitude of the
    field

3
Heres how we do it as easy as 1,2,3
  • Choose a Gaussian surface
  • a cylinder would work the field is - to the
    area vector on the sides and to the area vector
    on the top and the bottom of the cylinder
  • a cube or a parallelogram with sides to the
    surface would work, too
  • Evaluate the flux through the surface and the
    enclosed charge
  • EA EA 2EA
  • Qencl s A
  • Apply Gausss law
  • E s/ 2e0

The electric field of an infinite plane of charge
does NOT depend on the distance from the plane,
but ONLY on the surface charge density
4
Now add a second plane with opposite charge
parallel plate capacitor
  • For the negatively charged plane
  • Flux - 2EA
  • Charge -s A
  • E s/ 2e0 , pointing towards the plane
  • Use superposition to find the field between the
    plates and outside the plates
  • E0 , outside the plates
  • E s/ e0
  • Direction from to -

5
Use the properties of conductors and Gausss law
expel the field from some region in space
6
Electric field shielding has multiple uses
  • If you want to measure the gravitational force
    between 2 objects (Cavendish balance), you need
    to make sure that electric forces dont distort
    your measurement
  • Put the one of the objects in a light weight
    metal mesh (Faraday cage) to screen any stray
    electric fields
  • Use a coaxial cable ( has a central conductor
    surrounded by a metal braid which is connected to
    ground) to transmit sensitive electric signals

7
OK, we know how to get the Electric field in
almost any configuration, but what does this tell
us about how objects in nature interact ?
  • Well, we know the definition
  • Electric field Force/unit charge
  • So if we know E, we can find the force on a
    charge that is placed inside the field
  • We can use F ma and kinematics to find how this
    charge will move inside the field ( we did this
    for homework)
  • Today we will use conservation of energy a
    very powerful approach !

8
Electric potential energy
  • The potential energy is a measure of the
    interactions in the system
  • Define the change in potential energy by the
    WORK done by the forces of interaction as the
    system moves from one configuration to another
  • Electric force is a conservative force the work
    doesnt depend on the path taken, but only on the
    initial and final configuration gt Conservation
    of energy

9
How can the path not matter ?
Well, the work is not just Force multiplied by
displacement, it is the SCALAR Product between
the two.
10
Electric potential energy in a uniform field a
charge inside a parallel plate capacitor
11
The potential energy of two point charges
  • The force is along the radius
  • The work ( and the change in the potential
    energy) depends only on the initial and final
    configuration
  • The potential energy depends on the distance
    between the charges

12
If we have a collection of charges
13
Graph the potential energy of two point charges
  • U depends on 1/r and on the relative sign of the
    charges
  • Defined up to a constant. We take U 0 when the
    charges are infinitely far apart. Think of it as
    no interaction.

14
Conservation of Energy in 2 charge system
  • Total mechanical energy Emech const
  • Emech gt 0 , the particles can escape each other
  • Emech lt 0, bound system

15
2 examples ( done on the blackboard)
  • Distance of closest approach for 2 like charges
  • Escape velocity for 2 unlike charges
Write a Comment
User Comments (0)
About PowerShow.com