Notes: Electric Fields (20.4-20.5, 20.7)
The Field Model
How does one charge “know” that another charge is near and therefore feel a force from
that charge? How is the force transmitted through empty space from one charge to
another?
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.
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Electric Field
The Force Model: One charge exerts a force
directly on another force.
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.
A charge (or group of charges), known as the “source charges”, alter the space around
them by creating an electric field.
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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.
Other field models:
 alteration of space around a mass:
 alteration of space around a magnet:
The electric field can also be referred to as the force-to-charge ratio, calculated by:
Units:
Direction is defined as:
Summary
Notes: Electric Fields (20.4-20.5, 20.7), cont.
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?
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?
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 acceleration.
Electrophoresis
Summary
Notes: Electric Fields (20.4-20.5, 20.7), cont.
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.
1. 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.
2. 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.
3. 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.
4. 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 of a Point
Charge
Sample Problem
Summary
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 to the left of the point charge.
Notes: Electric Fields (20.4-20.5, 20.7), cont.
Superposition
The electric field due to multiple charges is the vector sum of the electric field due to
each of the charges.
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 P?
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?
Summary
A particle bearing -5.0 μC is placed at -2.0 cm, and a particle bearing 5.0 μC is placed at 2.0 cm. What is
the field at the origin?
A particle bearing 10.0 mC is placed at the origin, and a particle bearing 5.0 mC is placed at 1.0 m.
Where is the field zero?