Transcript Chapter 22 Electric Field

Chapter 22 Electric Field
22.1. What is Physics?
22.2. The Electric Field
22.3. Electric Field Lines
22.4. The Electric Field Due to a Point Charge
22.5. The Electric Field Due to an Electric Dipole
22.6. The Electric Field Due to a Line of Charge
22.7. The Electric Field Due to a Charged Disk
22.8. A Point Charge in an Electric Field
22.9. A Dipole in an Electric Field
The Electric Field
We bring in a positive
charge q0 as a test
charge, which is
carefully selected with
a very small
magnitude, so that it
does not alter the
locations of the other
charges
How does particle q0 “know” of the presence of other charge?
THE ELECTRIC FIELD
The electric field E that exists at a
point is the electrostatic force F
experienced by a small test charge q0
placed at that point divided by the
charge itself:
The electric field is a vector, and its
direction is the same as the direction of
the force F on a positive test charge
•
SI Unit of Electric Field: newton
per coulomb (N/C)
•
Important about electric field
• It is the surrounding charges that create an electric
field at a given point.
• Any charge q placed at the point with the electric field
E will experiences a force, F=qE. For a positive charge,
the force points in the same direction as the electric
field; for a negative charge, the force points in the
opposite direction as the electric field.
• At a particular point in space, each of the surrounding
charges contributes to the net electric field that
exists there
Example 1. Electric Field Leads to a Force
In Figure a the charges on the two metal spheres and
the ebonite rod create an electric field E at the spot
indicated. This field has a magnitude of 2.0 N/C and
is directed as in the drawing. Determine the force on
a charge placed at that spot, if the charge has a value
of (a) q0=+18×10–8 C and (b) q0=–24×10–8 C.
Example 2. Electric Fields Add as Vectors Do
Figure shows two charged
objects, A and B. Each
contributes as follows to
the net electric field at
point P: EA=3.00 N/C
directed to the right, and
EB=2.00 N/C directed
downward. Thus, EA and EB
are perpendicular. What is
the net electric field at P?
Example 3. The Electric Field of a Point Charge
There is an isolated point charge of q=+15
μC in a vacuum. Using a test charge of
q0=+0.80 μC, determine the electric field
at point P, which is 0.20 m away.
Properties of electric field by a point charge
(1) The magnitude of electric field by a point charge is given by
(2) If q is positive, then E is directed away from q, as in Figure
b. On the other hand, if q is negative, then E is directed
toward q.
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?
Example 4. The Electric Fields from
Separate Charges May Cancel
Two positive point charges, q1=+16 μC and
q2=+4.0 μC, are separated in a vacuum by a
distance of 3.0 m, as Figure illustrates. Find
the spot on the line between the charges
where the net electric field is zero.
Example 5. Vector properties of Electric Fields
Two point charges are lying on the y axis in
Figure a: q1=–4.00 μ C and q2=+4.00 μ C. They
are equidistant from the point P, which lies on
the x axis. (a) What is the net electric field
at P? (b) A small object of charge q0=+8.00 μ C
and mass m=1.20 g is placed at P. When it is
released, what is its acceleration?
Electric Field Lines
The electric charges create
an electric field in the
space surrounding them. It
is useful to have a kind of
“map” that gives the
direction and indicates the
strength of the field at
various places. This can be
done by drawing the
electric field lines.
Positive charged an infinitely large,
nonconducting sheet
The properties of the electric field lines
• At any point, the tangent direction of the electric line is the
direction of electric field.
• The density of the electric field lines provides information
about the magnitude of the field. The lines are closer
together where the electric field is stronger, the lines are
closer together. The lines are more spread out where the
electric field is weaker.
• The electric field lines always begin on a positive charge
and end on a negative charge and do not start or stop in
midspace.
Electric Dipole
• two charged particles of magnitude q but of
opposite sign, separated by a distance d.
We call this configuration an electric dipole
•
The product qd, which involves the two
intrinsic properties q and d of the dipole, is
the magnitude p of a vector quantity known
as the electric dipole moment of the
dipole. The direction of P is taken to be
from the negative to the positive end of the
dipole
The Electric Field Due to an Electric Dipole
For z>>d,
The Electric Field Inside a
Conductor: Shielding
(1) At equilibrium under
electrostatic conditions,
any excess charge
resides on the surface of
a conductor.
Shielding continue…
(2). At equilibrium under electrostatic conditions, the electric field
is zero at any point within a conducting material.
(3). The electric field just outside the surface of a conductor is
perpendicular to the surface at equilibrium under electrostatic
conditions
The Electric Field Due to a Line of Charge
Name
Symbol
SI Unit
Charge
q
C
Linear charge density
λ
C/m
Surface charge density
σ
C/m2
Volume charge density
ρ
C/m3
Electric field of a ring of uniform
positive charge
The Electric Field Due to a Charged Disk
For infinite sheet, R∞,
Sample Problem: A Point Charge in an Electric Field
Figure shows the deflecting plates of an ink-jet printer, with
superimposed coordinate axes. An ink drop with a mass m of 1.3x10-10
kg and a negative charge of magnitude Q=1.5x10-13 C enters the
region between the plates, initially moving along the x axis with
speed vx=18 m/s. The length L of each plate is 1.6 cm. The plates are
charged and thus produce an electric field at all points between
them. Assume that field E is downward directed, is uniform, and has
a magnitude of 1.4x106 N/C. What is the vertical deflection of the
drop at the far edge of the plates? (The gravitational force on the
drop is small relative to the electrostatic force acting on the drop
and can be neglected.)
A Dipole in an Electric Field
Potential Energy of an Electric Dipole
(choose θ=90o as a reference point):
Sample Problem
A neutral water molecule H2O in its vapor state has an
electric dipole moment of magnitude 6.2x10-30 c.m.
(a) How far apart are the molecule's centers of
positive and negative charge?
(b) If the molecule is placed in an electric field of
1.5x104N/c , what maximum torque can the field
exert on it? (Such a field can easily be set up in the
laboratory.)
(c) How much work must an external agent do to rotate
this molecule by 180o in this field, starting from its
fully aligned position, for which θ=0?
Conceptual Questions
(1)
(2)
(3)
A proton and an electron are held in place on the x axis. The
proton is at x=–d, while the electron is at x=+d. They are
released simultaneously, and the only force that affects their
motions is the electrostatic force of attraction that each
applies to the other. Which particle reaches the origin first?
Give your reasoning.
On a thin, nonconducting rod, positive charges are spread
evenly, so that there is the same amount of charge per unit
length at every point. On another identical rod, positive
charges are spread evenly over only the left half, and the
same amount of negative charges are spread evenly over the
right half. For each rod, deduce the direction of the electric
field at a point that is located directly above the midpoint of
the rod. Give your reasoning.
There is an electric field at point P. A very small charge is
placed at this point and experiences a force. Another very
small charge is then placed at this point and experiences a
force that differs in both magnitude and direction from that
experienced by the first charge. How can these two different
forces result from the single electric field that exists at
point P?
(4) Drawings I and II show two examples of electric field lines.
Decide which of the following statements are true and which
are false, defending your choice in each case. (a) In both I and
II the electric field is the same everywhere. (b) As you move
from left to right in each case, the electric field becomes
stronger. (c) The electric field in I is the same everywhere
but becomes stronger in II as you move from left to right. (d)
The electric fields in both I and II could be created by
negative charges located somewhere on the left and positive
charges somewhere on the right. (e) Both I and II arise from
a single positive point charge located somewhere on the left.
(5) A positively charged particle is moving horizontally
when it enters the region between the plates of a
capacitor, as the drawing illustrates. (a) Draw the
trajectory that the particle follows in moving through
the capacitor. (b) When the particle is within the
capacitor, which of the following four vectors, if any,
are parallel to the electric field inside the capacitor:
the particle’s displacement, its velocity, its linear
momentum, its acceleration? For each vector explain
why the vector is, or is not, parallel to the electric
field of the capacitor.