Title: PHYS117B: Lecture 6 Electric field in planar geometry. Electric potential energy.
1PHYS117B 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
2The 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
3Heres 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
4Now 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 -
5Use the properties of conductors and Gausss law
expel the field from some region in space
6Electric 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
7OK, 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 !
8Electric 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
9How can the path not matter ?
Well, the work is not just Force multiplied by
displacement, it is the SCALAR Product between
the two.
10Electric potential energy in a uniform field a
charge inside a parallel plate capacitor
11The 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
12If we have a collection of charges
13Graph 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.
14Conservation 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
152 examples ( done on the blackboard)
- Distance of closest approach for 2 like charges
- Escape velocity for 2 unlike charges