PHY 184

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PHY 184

• Week1 - Spring 2007
• Lecture 4

Title The Electric Field
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Announcements

• Clicker registration in lon-capa closes on
  January 22.
• Helproom schedule
• see LON-CAPA
• Stay after the lecture today for the Honors
  Option.

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Review - Coulombs Law

• The electric force F between two charges, q1 and
  q2, separated by a distance r is given by
  Coulombs Law
• 1/r2 dependence
• The constant k is called Coulombs constant and
  is given by

Opposite charges F is attractive (-) Like
charges F is repulsive ()
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E field QUALITATIVE
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The Electric Field
Field Theory The electric force is not action at
a distance but is the action of a field. A
field is a physical entity that extends
throughout a volume of space and exerts
forces. Electric field E(x,t) Magnetic field
B(x,t)
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The Electric Field (2)

• A charge creates an electric field around itself
  and the other charge feels that field.

Electric field at a given point in space place a
positive test charge q at the point and measure
the electrostatic force that acts on the test
charge then
Test charge point object with a very small
positive charge so that it does not modify the
original field
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The Electric Field (3)

• A field is not just an abstract concept that we
  use to describe forces. The field is real.
• The electric field extends throughout space and
  exerts forces on charged particles.
• If we place a positive point charge in an
  electric field, there will be a vector force on
  that charge in the direction of the electric
  field
• The magnitude of the force depends on the
  strength of the electric field.

Field theory versus action at a distance.
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E field QUANTITATIVE
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Precise Definition of Electric Field

• We define the electric field in terms of the
  force it exerts on a positive point charge
• Unit of the electric field N/C (newtons per
  coulomb)
• We can then write
• Note that the electric force is parallel to the
  electric field and is proportional to the charge
• The force on a negative charge will be in the
  opposite direction

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Example Field of a point charge

• What is the field created by a point charge q?
• Consider a test charge q0 at point x.
• Force on q0
• Electric field at x

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Superposition of Electric Fields

• Suppose we have many charges.
• The electric field at any point in space will
  have contributions from all the charges.
• The electric field at any point in space is the
  superposition of the electric field from n
  charges is
• Note that the superposition applies to each
  component of the field (x, y, z).

(vectors!)
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Electric Field Lines
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Electric Field Lines

• We can represent the electric field graphically
  by electric field lines i.e., curves that
  represent the vector force exerted on a positive
  test charge.
• Electric field lines will originate on positive
  charges and terminate on negative charges.
• Electric field lines do not cross. (Why?)
• The electric force at a given point in space is
  tangent to the electric field line through that
  point.

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Example
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Properties of Field Lines

• The strength of the electric field is represented
  by the density of electric field lines
• The direction of the electric field is tangent to
  the electric field lines

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Field Lines from a Point Charge

• The electric field lines from a point charge
  extend out radially.
• For a positive point charge, the field lines
  point outward
• Terminate at infinity
• For a negative charge, the field lines point
  inward
• Originate at infinity

3D
2D
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Electric Field Lines for Two Point Charges

• We can use the superposition principle to
  calculate the electric field from two point
  charges.
• The field lines will originate from the positive
  charge and terminate on the negative charge.

2d
3d
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Determine the direction of E(x) for points on the
plane half-way between the charges.
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Electric Field Lines from Identical Point Charges

• The electric field from two identical point
  charges
• For two positive charges, the field lines
  originate on the positive charges and terminate
  at infinity.
• For two negative charges, the field lines
  terminate on the negative charges and originate
  at infinity.

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Determine the direction of E(x) for points on the
plane half-way between the charges.
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General Observations about Field Lines

• If the field lines connect, we have an attractive
  force
• Imagine the charges pulling on each other
• If the field lines seem to spread out, we have a
  repulsive force
• Imagine the charges pushing each other apart

• Field lines always originate on positive charge
  and terminate on negative charge.
• Field lines never cross.

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Quiz

• Identify the charges (positive or negative) in
  the configuration

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Demo - Electric Field Lines

• Demo - visualization of electric field lines

The charge of grass seeds is redistributed by
induction. The Coulomb force makes the seeds
align along the field lines.
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Summary
E(x) F/q (definition) E sum of Ei
(superposition) The electric force on a charged
particle q located at position x is F q
E(x). The electric force is a field effect not
action at a distance.