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Electric Fields
If nothing existed to experience the
gravitational field of Earth, would the field still
How do we describe the gravitational field of
If we introduce an object to the gravitational
field of Earth, how can we determine what
force it will experience?
Force Model vs. Field Model
We have assumed that one charge
exerts a force on another. However,
in the field model, it is the alteration
of space around one charge that is
the agent that exerts the force on the
second charge.
 The Force Model: One charge
exerts a force directly on another
 The Field Model: One charge
modifies the space around itself
and the second charge responds
to the altered space. The altered
space is the agent that then
exerts the force.
The Electric Field
A charge (or group of charges), known as the “source
charges”, alter the space around them by creating an
electric field.
Free space has a constant value of the permittivity that appears in
physical relationships.
The permittivity of matter has a value different from that of free space.
If another charge is placed in that electric field, it will
experience a force exerted by the field.
Field Models
Electric Fields – alteration of space around a
Gravitational Fields – alteration of space
around a mass
Magnetic Fields – alteration of space around
a “magnet”
Why use fields?
Forces exist only when two or more particles
are present.
Fields exist even if no force is present.
The field of one particle only can be
Fields as a Ratio
The force-to-charge
 Fe
Direction is defined as
the direction of the force
that a positive test
charge will experience.
The force-to-mass
Direction is defined as
the direction that a test
mass will experience.
Sample Problem
The electric field in a given region is 4000 N/C pointed toward the
north. What is the force exerted on a 400 μg styrofoam bead
bearing 600 excess electrons when placed in the field?
3.84 x 10-13 N, south
Sample Problem
A 400 μg styrofoam bead has 600 excess electrons on its surface.
What is the magnitude and direction of the electric field that will
suspend the bead in midair?
4.08 x 1010 N, down
Sample Problem
A proton traveling at 440 m/s in the +x direction enters an electric
field of magnitude 5400 N/C directed in the +y direction. Find the
5.17 x 1011 m/s2, up
The DNA fragments are
negatively charged because of
the phosphate group.
The electric field causes the
ma  F e FD
qE  FD
The larger pieces of DNA have a
smaller acceleration.
Electric Field Diagrams
Electric field vectors represent the electric
field at a single point in space in proximity to
a point charge.
We always draw field vectors based on the
force on a positive test (probe) charge.
Electric Field Diagrams
The electric field, a vector quantity, exists at every point in space.
Electric field diagrams show a sample of the vectors, but there is an
electric field vector at every point whether one is shown or not.
The arrow indicates the direction and strength of the field at the
point to which it is attached – at the point where the tail of the
vector is placed. The length of any vector is significant only relative
the lengths of other vectors.
Although we have to draw vectors across the page, an electric field
does not “stretch” from point to another. Each vector represents the
electric field at one point in space.
If the probe/test charge is positive, the electric force will point in
the same direction as the electric field vector. If the probe/test
charge is negative, the electric force will point in the opposite
direction of the field vector.
Electric Field Around a Positive Charge
Electric Field Around a Negative Charge
Spherical Electric Fields
The Electric Field surrounding a point charge or a
spherical charge can be calculated by:
E 
40 r
E: Electric Field (N/C)
k: 8.99 x 109 N m2/C2
q: Charge (C)
r: distance from center of charge q (m)
Remember that k = 1/(4πε0)
Sample Problem
There is an isolated point charge of q = +15 μC in a vacuum.
Determine the electric field at point P, which is 0.20 m away.
Thought Experiment
Imagine you have a small, positively charged pith ball hanging
from a string. If you hang it at various locations between these
two configurations of charged spheres, how will it behave?
When more than one charge contributes to
the electric field, the resultant electric field is
the vector sum of the electric fields
produced by the various charges.
Again, as with force vectors, this is referred to
as superposition.
Sample Problem
The figure shows two
charged objects, A and
B. Each contributes as
follows to the net electric
field at point P: EA=4.00
N/C directed to the right,
and EB=3.00 N/C
directed downward.
Thus, EA and EB are
perpendicular. What is
the net electric field at
Electric Dipoles
Sample Problem
A dipole consists of a positive and negative charge separated by 1.2
cm, as shown. What is the electric field strength at a point 1.2 cm to
the right of the positive charge?
Check Your Understanding
A positive point charge +q is fixed in
position at the center of a square, as
the drawing shows. A second point
charge is fixed to either corner B,
corner C, or corner D. The net
electric field at corner A is zero. (a)
At which corner is the second charge
located? (b) Is the second charge
positive or negative? (c) Does the
second charge have a greater, a
smaller, or the same magnitude as the
charge at the center?