Download equipotential surface

Electrical Energy and
Capacitance
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Concept of potential difference and
potential
Potential and potential energy for
point charges
Potentials and charged conductors
Equipotential surfaces to
capacitance
Clicker question I

A.
B.
C.
D.
If the distance between two negative
charges is decreased by a factor of 3,
the resultant force between the two
charges changes by what factor?
Decreases to
Decreases to
Increases by
Increases by
1/9
1/3
9
3
A question
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A.
B.
C.
D.
E.
A suspended object A is attracted to a
neutral wall. It is also attracted to a
positively charged object B. Which of the
following is true?
The object A is uncharged
It has a positive charge
It has a negative charge
It may be either charged positively or negatively
It may be either charged or uncharged
Polarization Forces
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A charge near a
neutral object can
move other charges.
Like charges move
away and unlike
move front. All
resulting in a net
attraction.
A weak force
+Q -Q
+Q
-Q
+Q
-Q
-q
Chapter 16:Lecture II
We have talked about
Electric Potentials.
qi
V = U/q = k
| ri |
i
Scalar (not a vector)
Adds like numbers.
 q1 q2 q3 q 4 
V  k  
  
 r1 r2 r3 r4 
-q1
q2
q3
-q4
F
 
E  F /q
E
 U 
Fx   
 x 
U
V U /q
V
The Electron Volt

The electron volt (eV) is defined as the
energy that an electron gains when
accelerated through a potential
difference of 1 V
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Electrons in normal atoms have energies of
10’s of eV
Excited electrons have energies of 1000’s of
eV
High energy gamma rays have energies of
millions of eV
1 eV = 1.6 x 10-19 J
Equipotential Surfaces

An equipotential surface is a
surface on which all points are at
the same potential
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No work is required to move a charge
at a constant speed on an
equipotential surface
The electric field at every point on an
equipotential surface is perpendicular
to the surface
Equipotentials and Electric
Fields Lines – Positive Charge
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The equipotentials
for a point charge
are a family of
spheres centered on
the point charge
The field lines are
perpendicular to the
electric potential at
all points
Equipotentials and Electric
Fields Lines – Dipole
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Equipotential lines
are shown in blue
Electric field lines
are shown in gold
The field lines are
perpendicular to
the equipotential
lines at all points
Application – Electrostatic
Precipitator
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It is used to remove
particulate matter from
combustion gases
Reduces air pollution
Can eliminate
approximately 90% by
mass of the ash and
dust from smoke
Recovers metal oxides
from the stack
Application – Electrostatic
Air Cleaner


Used in homes to reduce the
discomfort of allergy sufferers
It uses many of the same
principles as the electrostatic
precipitator
Application – Xerographic
Copiers

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The process of xerography is used
for making photocopies
Uses photoconductive materials

A photoconductive material is a poor
conductor of electricity in the dark
but becomes a good electric
conductor when exposed to light
The Xerographic Process
Application – Laser Printer
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The steps for producing a document on
a laser printer is similar to the steps in
the xerographic process
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Steps a, c, and d are the same
The major difference is the way the image
forms on the selenium-coated drum
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A rotating mirror inside the printer causes the
beam of the laser to sweep across the seleniumcoated drum
The electrical signals form the desired letter in
positive charges on the selenium-coated drum
Toner is applied and the process continues as in
the xerographic process
Capacitance
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A capacitor is a device used in a
variety of electric circuits
The capacitance, C, of a capacitor
is defined as the ratio of the
magnitude of the charge on either
conductor (plate) to the magnitude
of the potential difference between
the conductors (plates)
Capacitance, cont
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Q
C
V
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Units: Farad (F)
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1F=1C/V
A Farad is very
large
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Often will see µF or
pF
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V is the potential
difference across
a circuit element
or device
V represents the
actual potential
due to a given
charge at a given
location
Parallel-Plate Capacitor

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The capacitance of a device
depends on the geometric
arrangement of the conductors
For a parallel-plate capacitor
whose plates are separated by air:
A
C  o
d
Parallel-Plate Capacitor,
Example
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The capacitor consists of
two parallel plates
Each have area A
They are separated by a
distance d
The plates carry equal and
opposite charges
When connected to the
battery, charge is pulled off
one plate and transferred to
the other plate
The transfer stops when
Vcap = Vbattery
Electric Field in a ParallelPlate Capacitor
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The electric field
between the plates is
uniform
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Near the center
Nonuniform near the
edges
The field may be
taken as constant
throughout the
region between the
plates