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The Electric Field
The Concept of a Field
Computing the Electric Intensity
Electric Field Lines
Gauss’ Law
Applications of Gauss’ Law
Objectives
Describe the concept of a field
Compute electric intensity
Draw electric field lines
State and apply Gauss’ Law
The Concept of a Field
The magnitude of electric field intensity
E is proportional to the force exerted on
a point charge q.
F
E
q
The direction of the electric field intensity E
at a point in space is the same as the
direction in which a positive charge would
move if it were placed at that point.
E
+
+q
-
E
+q
Computing the Electric Intensity
Electric intensity from Coulomb’s
law:
kQ
E 2
r
k = 9 x 109 N·m2/C2
When more than one charge
contributes to the field, the resultant
field is the vector sum of the
contributions from each charge:
kQ
E 2
r
Electric Field Lines
Electric field lines exist around charges or objects
carrying a charge
Model to explain how forces can act at a distance
Represented by imaginary field lines (arrows)
Not the same as vectors, though
Begin on negative charges and terminate on positive
charges
Perpendicular to surface of charge
Electric Field Lines
Draw the electric field lines around this charge
–q
Electric Field Lines
–q
Electric Field Lines
Electric field lines are imaginary lines drawn in such a
manner that their direction at any point is the same as the
direction of the electric field at that point.
The direction of the
field line at any
point is the same as
the direction in
which a positive
charge would move
it placed at that
point.
The spacing of the field
lines must be such that
they are close together
where the field is strong
and far apart where the
field is weak.
Electric Field Lines
Draw the electric field lines around this charge
+q
Electric Field Lines
+q
Gauss’ Law
The electric field intensity at a point in the
kq
E 2
center of an imaginary sphere is give by:
r
The permittivity of free space is
defined by:
1
e0 
 8.85  10 -12 C 2 / N  m2
4 pk
Gauss’s law:
The net number of electric lines of force
crossing any closed surface in an outward N   e 0 E nA   q
direction is numerically equal to the net
total charge within that surface.
Applications of Gauss’ Law
Charge density is the charge per unit area of
surface:
q

A
Summary of New Terms
•electric field
•electric field intensity
•electric field lines
•permittivity
•charge density
•Gauss’s law
•gaussian surface
•Faraday’s ice pail
Summary of Equations
F
E
q
kQ
E 2
r
kq
E 2
r
1
e0 
 8.85  10 -12 C 2 / N  m2
4 pk
N   e 0 E nA   q
q

A
Electric Field Lines
Draw the electric field lines around these charges
+q
+q
Electric Field Lines
Draw the electric field lines around these charges
+q
-q
Example
• What is the magnitude of the electric field
strength at a point in a field where a force of
1.0 N is exerted on an electron?
Example
Fe  1.0 N
q  160
. x10
-19
C
Fe
10
. N
18 N
E

 6.3x10
-19
C
q 160
. x10 C
Practice Problems
• Pg. 484 # 1 – 4