Physics 122B Electricity and Magnetism

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Physics 122B Electricity and Magnetism
Lecture 12 (Knight 30.1 to 30.4) Calculating E
from V April 23, 2007

• Martin Savage

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Lecture 12 Announcements

• Lecture HW Assignments 4 has been posted on
  the Tycho system. Assignment 4 is due at 10 PM,
  on Wednesday.
• Requests for regrades of Exam 1 should be
  written on a separate sheet (see Syllabus) and
  taken to Heleb Gribble in room C136 PAB. They
  will be accepted until noon on Wednesday.

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Chapter 29 Summary (1)
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Chapter 29 Summary (2)
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The Missing Link
How are E and V connected?
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Finding V from E
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Potential from the Fieldof a Point Charge
This is the same result that we obtained in
Chapter 29 from energy considerations.
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ExampleThe Potential of a Charged Disk
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Finding E from V
In other words, the E field components are
determined by how much the potential V changes in
the three coordinate directions.
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ExampleThe E Field of a Charged Ring
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ExampleFinding E from the Slope of V
An electric potential V in a particular
region of space where E is parallel to the x axis
is shown in the figure to the right. Draw Ex
vs x.
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Question
Which graph of the electric potential V
describes the electric field shown?
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Geometry of Potential and Field
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Example Finding the E-Field from Equipotential
Surfaces
The figure shows a contour map of a
potential. Estimate the strength and
direction of the electric field at points 1, 2,
and 3.

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Kirchhoffs Loop Law
Since the electric field isconservative,
any path betweenpoints 1 and 2 finds the same
potential difference. Any path can be
approximated by segments parallel and
perpendicular to equipotential surfaces, and the
perpendicular segments must cross the same
equipotentials. Since a closed loop starts
and ends at the same point, the potential around
the loop must be zero. This is Kirchhoffs Loop
Law, which we will use later.
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Question
Which set of equipotential contours
describes the electric field shown?
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A Conductor inElectrostatic Equilibrium
A conductor is in electrostatic equilibrium
if all charges are at rest and no currents are
flowing. In that case, Einside0. Therefore,
all of it is at a single potential
Vinsideconstant.
Rules for conductor.
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Sources of Electric Potential
A potential difference can be created by
moving charge from one conductor to another.
The potential difference on a capacitor can
produce a current (flow of charge), but this
current cannot be sustained because the charge
separation and potential difference rapidly
disappears.
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The Van de Graaff Generator

• A Van de Graaff Generatorpumps charge on a
  movingbelt, creating a large potential
  difference.
• Charge is mechanicallytransported from the
  negativeside to the positive side and sustains
  a potential differencebetween the spherical
  domeelectrode and its surroundings.
• The electric field of the dome exerts a
  downward force on the positive charges moving up
  the belt, causing the belt motor to do increasing
  work as the system charges. The work goes into
  lifting the positive charges through the rising
  field.

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Batteries and EMF
A battery is a chemical source of electric
potential difference. Chemical reactions create
potential difference by moving positive ions to
one electrode and negative ions to the other.
The system can be visualized as a chemical
charge escalator in which positive charges are
lifted through a potential difference. The
potential difference DVbat is determined by the
chemistry of the electrodes (e.g., carbon and
zinc) and remains essentially constant until the
chemicals are exhausted and the battery is
dead. The term EMF (electromotive
force),symbol E, is used to describe the work
done per unit charge by the battery E Wchem/q
DVbat. A real battery has internal
resistance that increases as the chemicals are
used and limits current flow.
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E Fields and Pointed Objects
On conductors, mobile charge tends to accumulate
at locations having the greatest curvature. This
creates very strong electric fields near the tip
of a pointed object. If such an object is
negatively charged, electrons may be field
emitted from the sharp point.
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Capacitors and Capacitance
Capacitance
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Example Charging a Capacitor

• The spacing between the plates of a 1.0 mF
  capacitor is 1 mm.
• What is the surface area A of the plates?
• How much charge is on the plates if this
  capacitor is attached to a 1.5 V battery?

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Forming a Capacitor
Any two conductors can form a capacitor,
regardless of their shape.
The capacitance depends only on the
geometry of the conductors, not on their present
charge or potential difference.
(In fact, one of the conductors can be moved
to infinity, so the capacitance of a single
conductor is a meaningful concept.)
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Example A Spherical Capacitor
A metal sphere of radius R1 is inside and
concentric with a hollow metal sphere of inner
radius R2. What is capacitance of this spherical
capacitor?
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Combining Capacitors
Parallel Same DV, but different Qs.
Series Same Q, but different DVs.
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Reminder Combining Resistors
Conducting material that carries current
across its length can form a resistor,a circuit
element characterized by anelectrical resistance
R R rL/Awhere L is
the length of the conductor and A is its cross
sectional area. R has units of ohms.
Multiple resistors may be combined in series,
where resistances add, or in parallel, where
inverse resistances add.
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Example A Capacitor Circuit
Find the charge and potential difference across
each capacitor shown in the figure.
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Energy Stored in a Capacitor
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End of Lecture 12

• Before the next lecture, read Knight, sections
  30.6 and 30.7.
• Lecture HW Assignments 4 has been posted on the
  Tycho system. Assignment 4 is due at 10 PM, on
  Wednesday .
• Requests for regrades of Exam 1 should be
  written on a separate sheet (see Syllabus) and
  taken to Helen Gribble in room C136 PAB. They
  will be accepted until noon on Wednesday.