Unformatted text preview: Physics 142 7/26/2011 Dielectrics
In electrical systems, we want to store as large a
charge separation as we can, but creating potential
differences is expensive. We would like to find
ways of reducing ∆V while keeping Q the same.
In biological systems, we often have charge
separations, but the are almost always separated
by spaces containing fluids – not by empty space.
It turns out that the answer to the first problem is
provided by the second observation. Physics 142 Summer 2011 Consider what happens
with an insulator
We know that
even with an insulator.
This reduces the field
inside the material,
just not to 0.
The field reduction factor is
defined to be κ.
Einside material = Eif no material were there κ E
– Physics 142 Summer 2011 Capacitors filled
with an insulating material
E= 1σ κ ε0 +–
+– Q κε 0 A d
∆V = Ed = κε A Q 0
C =κ 0
+– 0 Physics 142 Summer 2011 Dr. Nick Cummings 1 Physics 142 7/26/2011 Dielectrics
If nonIf a non-conductor is put between the
plates, there is still some polarization
reducing the field so the voltage
required for a given charge is
reduced, i.e., C is increased.
The factor (assuming the space
between the plates is filled) is called
the dielectric constant, κ. C =κ ε0A
d Physics 142 Summer 2011 What’s going on?
When we hook up a battery
(or any other electric power
source) and a bulb, the bulb
glows but after a little start
up time, stays at a constant
We want to understand
what’s going on here. Physics 122 Electrical Current
This effect will involve large amounts of
charge particles moving together. This motion
of charges is called electrical current.
Need to quantify the motion of charges
Usually we’ll be concerned with charges
moving inside a material
– Need to understand how that works Physics 122 Dr. Nick Cummings 2 Physics 142 7/26/2011 Moving Charges
in a Neutral Conductor
What happens if we arrange charges to put an electric
force on a neutral conductor?
– Positive ions are fixed in a lattice
– Some negative charges (shared electrons) are free to move Physics 122 Conductivity in a metal is complicated –
and involves the quantum nature of electrons
What really happens is quantum mechanical – like
covalent bonding. nuclei Shared
cloud Physics 122 Conduction
In a crystal of a metal, all the atoms are
bonded and some electrons shared. You
You can think of some of the electrons as
running in each direction along the chain.
When an electric field is put on the chain, is
shifts the balance and more electrons go one
way than the other.
Physics 122 Dr. Nick Cummings 3 Physics 142 7/26/2011 How to think about current?
Unless we are going to be materials science
physicists, we don’t really need to understand the
quantum view of conduction.
Instead, we construct a bunch analogies
that have some of the correct features.
– water flow
– air flow These
These help us make sense of the fundamental laws
that govern current flow. Physics 122 The fluid flow model
Key concept: Pressure
Recall: 1 2
– Pressure is like a tension but in 3D.
– It pushes in all directions at once,
so it has no direction.
– Forces due to pressure occur when you
only let it push on one side of an area. Then r
F = PA
Physics 122 Viscous Drag
A fluid flowing in a pipe doesn’t slip through the
The fluid sticks to the walls moves faster at the
middle of the pipe than at the edges.
As a result, it has to “slide over itself” (shear).
There is friction between layers of fluid moving at
different speeds that creates a viscous drag force,
trying to reduce the sliding.
The drag is proportional to the speed and the
length of pipe. Fdrag = 8πµLv Physics 122 Dr. Nick Cummings 4 Physics 142 7/26/2011 Implication: Pressure drop
If we have a fluid moving at a constant rate
and there is drag, N2 tells us there must be
another force to balance the drag.
The internal pressure in the fluid must drop
in the direction of the flow to balance drag.
Flow in Flow out
Pressure force Pressure force
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