Download E vector N/C Newton per Coulomb

12/15/2015
Chapter 15 Lecture
The Electric Field
A model of the mechanism for electrostatic
interactions
 A model for electric
interactions, suggested by
Michael Faraday, involves
some sort of electric
disturbance in the region
surrounding a charged
object.
 Physicists call this electric
disturbance an electric
field.
© 2014 Pearson Education, Inc.
GRAVITATIONAL FORCE vs.
ELECTROSTATCS FORCE
OBJECT WITH MASS
GRAVITATIONAL FORCE vs.
ELECTROSTATCS FORCE
OBJECT WITH MASS
ELECTRIC FIELD
PHYSICAL QUANTITY:
ELECTRIC FIELD
+Q
Electric field is a property of a location in
space that measures the force per unit
charge that a charged object would feel
if placed at that location.
 Symbol
E
 Units
Newton per Coulomb
 Units symbol
N/C
 Type of PQ
vector
1
12/15/2015
Your diaper, your field !!
ELECTRIC FIELD DUE TO A SINGLE
POINT-LIKE CHARGED OBJECT
ELECTRIC FIELD DUE TO A SINGLE POINTLIKE CHARGED OBJECT
WHITEBOARD
ELECTRIC FIELD DUE TO A SINGLE POINTLIKE CHARGED OBJECT
 We can interpret this field as follows:
 The E field vector at any location points away
from the object creating the field if Q is positive,
and toward the object creating the field if Q is
negative.
 3. A, B, & C are random points around a +2C
electric charge.
•
1. What is the strength and direction of the
electric field 0.4 m away from a -9.0C electric
charge?
•
2. At what distance from a –5.5 C electric
charge would the electric field strength be
1.90x105 N/C ?
Somebody else’s diaper, somebody
else’s field !
 Find the intensity of the electric field produced by
the electric charge at points A, B, & C.
 Assume each box to be d = 0.1 m
C
A
+
+2C
B
2
12/15/2015
ELECTRIC FIELD FELT BY AN
ELECTRIC CHARGE
ELECTRIC FIELD FELT BY AN ELECTRIC
CHARGE INSIDE A UNIFORM E-FIELD
A 5C electric charge is placed inside a uniform electric field.
Fq =
k·qA·qB
d2
a. If an electric force of 0.07 N is exerted on the electric
charge, what is the magnitude of the electric field?
b. What electric force would be exerted if charge A is
substituted by an electric charge of -4C?
F
E= qq
c. What would the magnitude of a new electric charge be, if
an electric force of 0.063 N is exerted on it?
E
qA
+
ELECTRIC FIELD LINES
(E-Field Lines)
 E-Field lines are a graphic representation of
electric fields used by physicists to study
and analyze electric fields.
Experiment: Grass seeds placed near a charged
object.
Observation: Grass seed aligned in a specific
pattern of lines surrounding the charged object.
ELECTRIC FIELD LINES
Electric Field lines point in the direction of
the electric field.
Electric field lines do not exist but they are
useful when analyzing electric fields.
ELECTRIC FIELD LINES
q
PROPERTY 1
 E-field lines start (leave) on positive charges.
 E-field lines end (enter) on negative charges.
2q
PROPERTY 2
The number of electric field lines is
proportional to the magnitude of the charge.
The bigger the magnitude of the electric
charge the more the amount of E-field lines.
3
12/15/2015
ELECTRIC FIELD LINES
PROPERTY 3
E field lines
E-Field lines will NOT cross
each other
© 2014 Pearson Education, Inc.
ELECTRIC FIELD LINES
ELECTRIC FIELD LINES
Grass seeds in an insulating liquid align with a
similar electric field produced by two
oppositely charged objects
Grass seeds in an insulating liquid align with a
similar electric field produced by two objects
with the same charge
PROPERTIES
WHITEBOARD
In which direction would the electric field be at each point?
A
B
C
D
4
12/15/2015
WHITEBOARD
In which direction would the electric field be at each point?
d
+Q
What is the magnitude and
direction of the electric field at
X?
E=0
d/2
d/2
+Q
WHITEBOARD
USING THE SUPERPOSITION PRINCIPLE
-Q
Each charged particle contributes an amount
k
-Q
Q
( d2 )2
 Draw E field lines for a large, uniformly charged
plate of glass at a random point in front of the
plate.
to the field at the center.
Using some vector
addition gives us
the net result
E=
8kQ
d2
to the
right
© 2014 Pearson Education, Inc.
5
12/15/2015
WHITEBOARD
ELECTRIC FIELD
USING THE SUPERPOSITION PRINCIPLE
1. Draw the direction of the electric field created by charge
Q at point P.
2. Draw the direction of the electric field created by charge
q at point P.
3. Draw the direction of the Net Electric field at point P.
WHITEBOARD
ELECTRIC FIELD
USING THE SUPERPOSITION PRINCIPLE
1. Draw the direction of the
Net Electric field at point
P.
2. Find the magnitude of the
electric field at point P.
1 box = 0.1 m
q = -4µC
WHITEBOARD
ELECTRIC FIELD
USING THE SUPERPOSITION PRINCIPLE
1. Draw the direction of the
Net Electric field at point
P.
WHITEBOARD
ELECTRIC FIELD
USING THE SUPERPOSITION PRINCIPLE
1. Draw the direction of the Net Electric field at point P.
2. Write an expression for the magnitude of the electric
field at point P.
2. Find the magnitude of the
electric field at point P.
1 box = 0.1 m
qA = +4µC
qB = -4µC
WHITEBOARD
CONSTANT ELECTRIC FIELDS
1. Draw the direction of the Electric field between two
parallel charged plates..
• Draw the path that a
negatively
particle
charged
will
follow
through the parallel
charged plates.
6
12/15/2015
ELECTRIC FIELD DEFLECTS AN INK BALL
WHITEBOARD
 Draw a force diagram (see picture next
slide)
 Find the magnitude of all forces exerted on
the ink ball.
 Find the time it takes the ink ball to go
through the parallel plates.
 Find the vertical acceleration of the ink
ball.
 Find the vertical displacement the ink ball
is deflected so that it lands at a particular
spot on a piece of paper.
THE V FIELD
 Can we describe electric fields
MATHEMATICAL MODELS
(FOR ELECTRIC FORCE AND ELECTRIC
POTENTIAL ENERGY USE Q & q)
ELECTRIC FORCE
Divide
electric
force by
“q” 
using the concepts of work and
energy?
 To do so, we need to describe the
ELECTRIC
POTENTIAL ENERGY
electric field not as a force-related E
field, but as an energy-related field.
Divide
electric
potential
energy by
“q” 
ELECTRIC
FIELD 1
ELECTRIC
FIELD 2
ELECTRIC
POTENTIAL 1
ELECTRIC
POTENTIAL 2
© 2014 Pearson Education, Inc.
PHYSICAL QUANTITY:
ELECTRIC POTENTIAL
ELECTRIC POTENTIAL
+Q
Electric potential is a property of a
location in space that measures the
energy per unit charge that a charged
object would feel if placed at that
location.
 Symbol
V
 Units
Joules per Coulomb
(Volts)
 Units symbol
 Type of PQ
J/C
[v]
scalar
7
12/15/2015
THE V FIELD
THE V FIELD
 Both the V field and the E field at a
specific location are independent of
a test charge and characterize the
properties of space at that location.
© 2014 Pearson Education, Inc.
 E-field is a vector physical quantity.
Direction depends on the type of
charge.
 V-field is a scalar physical quantity.
It can have a negative or positive
value depending on the sign of the
electric charge Q of the object that
creates the field at a particular
location
© 2014 Pearson Education, Inc.
Potential difference V
 The value of the electric potential depends on the
choice of zero level, so we often use the
difference in electric potential between two points.
 The Electric Potential Difference V between two
points A and B is equal to the difference in the
values of electric potential at those points.
Particles in a potential difference
 A positively charged object accelerates from
regions of higher electric potential toward
regions of lower potential (like an object falling to
lower elevation in Earth's gravitational field).
 A negatively charged particle tends to do the
opposite, accelerating from regions of lower
potential toward regions of higher potential.
V = VB – VA
© 2014 Pearson Education, Inc.
© 2014 Pearson Education, Inc.
WHITEBOARD ELECTRIC POTENTIAL
• A, B, & C are random points around a +2C electric
charge.
• Find the electric potential produced by the electric
charge at points A, B, & C.
• Assume each box to be d = 0.1 m
+
+2C
 Two -3µC charged point like objects are
separated by 0.2 m. Determine the electric
potential at a point:
 A. halfway between the objects
 B. 0.2 m to the to the side of one of the
objects.
C
A
WHITEBOARD
B
© 2014 Pearson Education, Inc.
8
12/15/2015
WHITEBOARD
 Suppose that the heart's dipole charges −Q and
+Q are separated by distance d. Write an
expression for the V field due to both charges at
point A, a distance d to the right of the +Q
charge.
WHITEBOARD
 Four objects with the same charge –q are
placed at the corners of a square of side d.
 A. Sketch the situation. Identify the center of the
square.
 B. Determine the value of the Electric Field at a
point that is located in the center of the square
(sketch).
 C. Determine the value of the Electric Potential
at a point that is located in the center of the
square.
WHITEBOARD
 See picture on next slide.
 Inside an X-ray machine is a wire (called a
filament) that, when hot, ejects electrons.
Imagine one of those electrons, now located
outside the wire. It starts at rest and accelerates
through a region where the V field increases by
40,000 V. The electron stops abruptly when it
hits a piece of tungsten at the other side of the
region, producing X-rays. How fast is the
electron moving just before it reaches the
tungsten?
Equipotential surfaces: Representing
the V field
THE V-FIELD
 The lines represent surfaces of constant electric
potential V, called equipotential surfaces.
 The surfaces are spheres (they look like circles
on a two-dimensional page).
© 2014 Pearson Education, Inc.
9
12/15/2015
Equipotential surfaces: Representing
the V field
© 2014 Pearson Education, Inc.
Equipotential surfaces and E field
© 2014 Pearson Education, Inc.
Contour maps: An analogy for
equipotential surfaces
RELATING THE
V-FIELD AND
THE E-FIELD
© 2014 Pearson Education, Inc.
Deriving a relation between the E field and ΔV
Deriving a relation between the E field and ΔV
We attach a small object with
charge +q to the end of a very
thin wooden stick and place the
charged object and stick in the
electric field produced by the
plate.
WHITEBOARD
• Draw a Force Diagram
– Charge is the system
– Ignore force that Earth exerts on the charge.
– Charge is not accelerating
10
12/15/2015
Deriving a relation between the E field and ΔV
WHITEBOARD
• The “stick” moves away from the positively charged plate.
System is charge and electric field.
• Draw a force diagram.
• Draw a work-energy bar chart
Deriving a relation between the E field and
ΔV
 Applying the generalized work-energy equation,
we get:
 Equivalently, the component of the E field along
the line connecting two points on the x-axis is
the negative change of the V field divided by the
distance between those two points:
𝐸𝑥 = −
WHITEBOARD
 Ben brings a grounded metal sphere with a
wooden handle near a Van De Graaff generator
so that their potential is 450,000 v and the
sphere does not get charged.
 Ben pulls the sphere away. Predict the
magnitude of the electric field when you see a
spark.
∆𝑉
∆𝑥
Deriving a relation between the E field and
ΔV
 The direction of the E-field points
direction of decreasing V-field.
in the
 The relation between the E-field and the E-field
tells us:
 When V-field is constant, E-field is zero.
 Two points at a different potential, the closer
the points are, the stronger the E-filed will be.
WHITEBOARD
 Look at the two situation below (point P is
located halfway between both charges):
 Find Magnitude and direction of electric field
at point P.
 Find magnitude of electric potential at point P.
 Conclusions?
CONDUCTORS IN
ELECTRIC
FIELDS
11
12/15/2015
Electric field of a charged conductor
Electric field of a charged conductor
Electric field outside a charged conductor
Electric field inside/outside a charged
conductor
• Electric field is a vector
physical quantity.
• Electric field inside the
charged conductor cancel
each other out.
• E=0 inside the conductor
Electric potential inside/outside a charged
conductor
• Electric Potential is a scalar
physical quantity.
• Electric potential inside the
charged conductor add up.
• V>0 inside the conductor
Grounding
 Grounding discharges
an object made of
conducting material by
connecting it to Earth.
 Electrons will move
between and within the
spheres until the V field
on the surfaces of and
within both spheres
achieves the same
value.
© 2014 Pearson Education, Inc.
12
12/15/2015
Uncharged conductor in an electric field:
Shielding
 The free electrons inside the object become
redistributed due to electric forces, until the E
field within the conducting object is reduced to
zero.
© 2014 Pearson Education, Inc.
Uncharged conductor in an electric field:
Shielding
 The interior is protected from the external field—
an effect called shielding.
© 2014 Pearson Education, Inc.
Dielectric materials in an electric field
DIELECTRICS IN
ELECTRIC
FIELDS
 If an atom in a dielectric
material resides in a region
with an external electric
field, the nucleus and the
electrons are displaced
slightly
in
opposite
directions until the force
that the field exerts on each
of them is balanced by the
force they exert on each
other.
© 2014 Pearson Education, Inc.
Polar water molecules in an external electric
field
 Some molecules, such as water, are natural
electric dipoles even when the external E field is
zero.
© 2014 Pearson Education, Inc.
E field inside a dielectric
 A dielectric material cannot completely shield its
interior from an external electric field, but it does
decrease the field.
© 2014 Pearson Education, Inc.
13
12/15/2015
E field inside a dielectric
Dielectric constants for different types of
materials
 Physicists use a physical quantity to characterize
the ability of dielectrics to decrease the E field:
 The dielectric constant κ
© 2014 Pearson Education, Inc.
© 2014 Pearson Education, Inc.
Electric force and dielectrics
•
•
The force that object 1 exerts on object 2 is reduced by
κ compared with the force it would exert in a vacuum.
Inside the dielectric material, Coulomb's law is now
written as:
© 2014 Pearson Education, Inc.
Salt dissolves in blood but not in air
 When salt is placed in water or blood:
 Many more collisions occur between
molecules than between molecules and air;
these can break an ion free from the crystal.
 Any ions that become separated do not exert
nearly as strong as an attractive force on
each other because of the dielectric effect.
 The random kinetic energy of the liquid is
sufficient to keep the sodium and chlorine
ions from recombining, allowing the nervous
system to use the freed sodium ions to
transmit information.
© 2014 Pearson Education, Inc.
Tip
CAPACITORS
© 2014 Pearson Education, Inc.
14
12/15/2015
CAPACITORS
CAPACITORS
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
• A capacitor consists
of two conducting
surfaces separated by
a nonconducting
material.
+
-
• The role of a capacitor
is to store electric
potential energy.
BATTERY
A negatively charged particle
accelerates from regions of
lower
potential
toward
regions of higher potential
(more negative electric
potential).
Charges will stop moving
when the
V of the
battery is the same V of
the capacitor. This process
happens very quickly.
Capacitors (Cont'd)
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
+
-
+
+
-
-
+
-
+
-
+
-
+
-
+
-
-
+
-
Charged
capacitor
+
Capacitor in the
process of
charging
+
+
-
+
+
-
-
-
BATTERY
+
+
-
+
-
+
BATTERY
+
BATTERY
CAPACITANCE
•
When a capacitor is connected to an electric potential
CAPACITANCE
 The proportionality constant C in this equation is
called the capacitance of the capacitor.
difference, the two plates become charged one plate
acquires negative charge and the other plate positive
charge.
• The amount of charge acquired by each plate is:
C=
q
V
 The unit of capacitance is 1 coulomb/volt = 1 farad
(in honor of Michael Faraday).
15
12/15/2015
Capacitors
PHYSICAL QUANTITY:
CAPACITANCE
the ability of a conductor to
• Definition: store energy in the form of
electrically separated charges.
• Symbol: C
• Units: Farads (F)
C
q
V
 If we consider the capacitor plates to be large
flat conductors, charge should be distributed
evenly on the plates.
 The magnitude of the E field between the
plates relates to the potential difference from
one plate to the other and the distance
separating them
 To double the E field, the charge on other
plates has to double.
• Type of PQ: Scalar
© 2014 Pearson Education, Inc.
QUANTITIES THAT AFFECT THE CAPACITANCE
OF A CAPACITOR: PLATE AREA
 A capacitor with larger-surface-area plates
should be able to maintain more charge
separation because there is more room for the
charge to spread out.
QUANTITIES THAT AFFECT THE CAPACITANCE
OF A CAPACITOR: DISTANCE SEPARATION
 A larger distance between the plates leads to a smallermagnitude E field between the plates. Because the
magnitude of this E field is proportional to the amount of
electric charge on the plates, a larger plate separation
leads to a smaller-magnitude electric charge on the
plates.
© 2014 Pearson Education, Inc.
QUANTITIES THAT AFFECT THE CAPACITANCE
OF A CAPACITOR: DIELECTRIC CONSTANT
 Material between the plates with a large
dielectric constant becomes polarized by the
electric field between the plates. Thus more
charge moves onto capacitor plates that are
separated by material of high dielectric constant.
Capacitance of a capacitor
 The capacitance of a particular capacitor should
increase if the surface area A of the plates
increases, decrease if the distance d between
them is increased, and increase if the dielectric
constant k of the material between them
increases:
© 2014 Pearson Education, Inc.
16
12/15/2015
Tip
ELECTRIC WORK
W  q · v
© 2014 Pearson Education, Inc.
WHITEBOARD
MATHEMATICAL MODELS
ELECTRIC POTENTIAL ENERGY
Uq [ J ]
• A capacitor besides of storing electric
charge, also stores electric potential
energy.
W = Uq
Uq =
q · V
2
MATHEMATICAL MODELS
CAPACITANCE
C=
q
V
C
q · V
2
A
4kd
C · (V)
2
2
Uq =
C=
q
V
ELECTRIC POTENTIAL
ENERGY
Uq =
q · V
2
 Write a mathematical model for
Uq in terms of C and V
 Write a mathematical model for
Uq in terms of C and q
WHITEBOARD
MATHEMATICAL MODELS
ELECTRIC POTENTIAL ENERGY
Uq =
CAPACITANCE
Uq =
 Write a mathematical model for
E-field in terms of q, k, , A.
GAUSS LAW
(q)2
2·C
17
12/15/2015
WHITEBOARD
AP2 EQUATION TABLE
TEXTBOOK
 Estimate the capacitance of your physics
textbook, assuming that the front and back covers
(area A = 0.050 m2, separation d = 0.040 m) are
made of a conducting material. The dielectric
constant of paper is approximately 6.0.
 Determine what the potential difference must be
across the covers for the textbook to have a
charge separation of 10−6 C (one plate has charge
+10−6 C and the other has charge −10−6 C).
© 2014 Pearson Education, Inc.
POINT LIKE CHARGES
CAPACITORS
Uq = q · v
18