Download The Electric Field

PHY 184
Week1 - Spring 2007
Lecture 4
Title: The Electric Field
1/11/07
184 Lecture 4
1
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 - Coulomb’s Law
qq
F k
r
 The electric force F
1 2
between two charges, q1
2
and q2, separated by a
distance r is given by
Coulomb’s Law:
Opposite charges: F is attractive (-)
Like charges: F is repulsive (+)
 1/r2 dependence
 The constant k is called
Coulomb’s constant and is
given by
2
Nm
k  8.99  109 2
C
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or
k
1
40
184 Lecture 4
where
 0  8.85  1012
C2
Nm2
3
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.
+
+
Test charge q
Test charge: point object with a very
small positive charge so that it does
not modify the original field
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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

 F
E
q
6
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

 F
E
q

 
F  qE (x )
 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:

 
F
E (x ) 
q0
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
qq0
F  k 2 rˆ
r
q
 k 2 rˆ
r
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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
E  E1  E2    En
(vectors!)
 Note that the superposition applies to each
component of the field (x, y, z).
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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.
E(x)  F
 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.
q
Unique
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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
Weak
Strong
 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
3D
2D
• Originate at infinity
kq
E(x)  2 rˆ
r
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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
B
A
D
Positive: A, B, C
Negative D, E, F
E
F
C
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Demo - Electric Field Lines

Demo - visualization of electric field lines
-
Grass seeds
The charge of grass seeds is
redistributed by induction.
The Coulomb force makes the seeds
align along the field lines.
Coulomb
force
+
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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.
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