Transcript 22-1 Electric Field

Lecture PowerPoint
Physics for Scientists and
Engineers, 3rd edition
Fishbane
Gasiorowicz
Thornton
© 2005 Pearson Prentice Hall
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Chapter 22
Electric Field
Main Points of Chapter 22
• Electric field
• Superposition
• Electric dipole
• Electric field lines
• Field of a continuous distribution of charge
• Motion of a charge in a field
• Electric dipole in external electric field
22-1 Electric Field
Definition of electric field: force on small test
charge, divided by the magnitude of the charge:
(22-1)
Test charge must be small enough that it does
not affect field:
22-1 Electric Field
More properly, the electric field is defined:
(22-2)
Units of electric field: N/C (newtons per coulomb)
For a point charge, the electric force is:
(22-3)
22-1 Electric Field
Therefore, the electric field of a point charge is:
(22-5)
The field points outwards from a positive charge
and inwards to a negative one:
22-1 Electric Field
Once the electric field is known, can immediately
find the force on any point charge q′:
(22-7)
22-1 Electric Field
Since electric forces add by superposition, the
electric field does as well.
For a group of point charges:
(22-11)
22-1 Electric Field
An electric dipole is defined as equal and
opposite charges a distance L apart:
The electric dipole moment is defined as:
(22-13)
and points from the negative charge
towards the positive one.
22-1 Electric Field
The field of an electric dipole falls off faster than the
field of a single point charge; it decreases as 1/r3.
Electric dipoles are often found in nature. Charged
objects can induce electric dipoles (left); molecules
may have permanent electric dipole moments due to
their structure (right).
22-2 Electric Field Lines
Electric field lines are a useful aid to
visualizing the electric field. There are two
rules to drawing these lines:
1. The electric field is tangent to the field line at
every point.
2. The density of electric field lines is an
indicator of relative field strength.
The next slide shows field lines for a point
charge, including the decrease in density as one
moves farther from the charge.
22-2 Electric Field Lines
Field lines of a
positive point
charge:
22-2 Electric Field Lines
Electric field lines have certain properties which
should be carefully noted:
1. Lines can start or end only on charges.
2. The electric field lines of a point charge go off
to infinity, and by superposition this will be true
for any localized collection of charges with a
net charge.
22-2 Electric Field Lines
Electric field lines have certain properties which
should be carefully noted:
3. Electric field lines originate on, and run
outward from, positive charges. They run
toward, and terminate on, negative charges.
4. No two field lines ever cross, even when
multiple charges are present.
22-2 Electric Field Lines
Left: two equal, same-sign charges
Right: an electric dipole
Important note: We always draw only a few sample field
lines; otherwise the sketch would be solid color. There is
electric field between all the lines in these two examples
except for one point on the left-hand diagram.
22-3 The Field of a Continuous Distribution
To find the field of a continuous distribution of
charge, treat it as a collection of near-point
charges:
(22-17)
Summing over the
infinitesimal fields:
(22-18)
22-3 The Field of a Continuous Distribution
Finally, making the charges infinitesimally
small and integrating rather than summing:
(22-20)
Some types of charge distribution are relatively
simple.
Constant linear charge density
: (22-21)
(22-22)
22-3 The Field of a Continuous Distribution
Constant surface charge density
(22-24)
:
(22-23)
22-3 The Field of a Continuous Distribution
Constant volume charge density
(22-26)
:
(22-25)
22-3 The Field of a Continuous Distribution
From the electric field due to a uniform sheet of charge,
we can calculate what would happen if we put two
oppositely-charged sheets next to each other:
The individual fields:
The superposition:
The
result:
22-4 Motion of a Charge in a Field
While the electron is between the plates, it
experiences an acceleration in the y-direction:
22-4 Motion of a Charge in a Field
Specifically, the acceleration is:
(22-38)
The initial velocity is in the x-direction, so the
velocity as a function of time is:
(22-39)
The time taken by the charge to traverse the
plates is determined only by the initial velocity.
22-4 Motion of a Charge in a Field
Therefore, the particle’s deflection in the ydirection is:
(22-42)
It exits the field making an angle θ with its
original direction, where:
(22-43)
22-5 The Electric Dipole in an External
Electric Field
An electric dipole in a uniform electric field
will experience no net force, but may
experience a torque:
22-5 The Electric Dipole in an External
Electric Field
The torque then is:
(22-44)
Using the dipole moment:
(22-46)
Work done by the field:
(22-47)
Therefore the potential energy is:
(22-49)
Which can also be written:
(22-50)
Summary of Chapter 22
• Electric field is defined as the force per unit
charge:
(22-2)
• Force on a point charge q′:
(22-7)
• Electric field lines are very useful for visualizing
the electric field, as long as their limitations are
taken into account.
Summary of Chapter 22, cont.
• Electric field of a point charge:
(22-5)
• Electric fields obey the superposition principle.
• Electric dipole: equal and opposite charges
separated by a distance L. The electric field is
proportional to the dipole moment, which is:
(22-13)
Summary of Chapter 22, cont.
• An electric dipole in an external electric field
feels a torque, and has potential energy:
(22-46)
(22-50)
• Electric field due to a continuous charge
distribution:
(22-20)