Transcript 16.7 The Electric Field For a point charge

Chapter 16
Electric Charge and
Electric Field
Objectives: The students will be able to:
• Explain the concept of electric field and determine the
resultant electric field at a point some distance from two or
more point charges.
• Determine the magnitude and direction of the electric force
on a charged particle placed in an electric field.
16.7 The Electric Field
The electric field is the
force on a small charge,
divided by the charge:
(16-3)
Only need one charge
to have an electric field
unlike Coulomb’s Law.
Electric Field
Test charge q is always positive. Therefore the
direction on the force of the test charge would
be away from the main charge which shows
direction of the electric field.
Electric Field
Test charge q is always positive. Therefore the
direction on the force of the test charge would
be towards the main charge which shows
direction of the electric field.
Sample Problem 1 (similar to #23
page 466)
What are the magnitude and direction of
the electric force on an electron in a
uniform electric field of strength
2460N/C that points due East?
Sample Problem 1 (similar to #23
page 466)
What are the magnitude and direction of the electric
force on an electron in a uniform electric field of
strength 2460N/C that points due East?
Since the E electric field points east, the force on an
electron would point in the opposite direction, west. (The
F force on a proton would point in the same direction as
the E field).
Sample Problem 2 (similar to #24
page 466)
A proton is released in a uniform electric
field, and it experiences an electric force of
1.86 x 10-14N toward the south. What are
the magnitude and direction( north, east,
south, west) of the electric field?
Sample Problem 2 (similar to #24
page 466)
A proton is released in a uniform electric field, and it experiences an electric
force of 1.86 x 1014N toward the south. What are the magnitude and
direction( north, east, south, west) of the electric field?
Proton, positive charge, will always be attracted toward a negatively
charged plate/point. Field lines always point from positive to negative.
If it's being attracted south, negative charge must be somewhere south
of it, so field must be in a southward direction.
Sample Problem 3 (similar to #27
page 466)
What is the magnitude and direction of the
acceleration experienced by an electron in
and electric field of 600 N/C? How does the
direction of the acceleration depend on the
direction of the field at that point?
Sample Problem 3 (similar to #27 page 466)
What is the magnitude and direction of the acceleration experienced by
an electron in and electric field of 600 N/C? How does the direction of
the acceleration depend on the direction of the field at that point?
First, looking at the given information, we know we can find Force using E =
F/q. From there, you can easily find the acceleration using F = ma.
Given info:
E = 600 N/C
q = 1.602e-19
E = F/q
600 N/C = F/(1.602e-19)
F = 9.612e-17 N
F = ma
9.612e-17 N = (9.11e-31)a
a = 1.055e14 m/s/s
Because it's an electron, it has a negative charge. This means that the electron
should always accelerate in the opposite direction of the E. Field.
Homework
Page 466
Problems 25, 27, and 30
Objectives: The students will be able to:
Explain the concept of electric field and determine the
resultant electric field at a point some distance from two or
more point charges.
Determine the magnitude and direction of the electric force
on a charged particle placed in an electric field.
Sketch the electric field pattern in the region between
charged objects.
16.7 The Electric Field
For a point charge:
(16-4a)
(16-4b)
How to derive the equation
16.7 The Electric Field
Force on a point charge in an electric field:
(16-5)
Superposition principle for electric fields:
16.7 The Electric Field
Problem solving in electrostatics: electric
forces and electric fields
1. Draw a diagram; show all charges, with
signs, and electric fields and forces with
directions
2. Calculate forces using Coulomb’s law
3. Add forces vectorially to get result
Sample Problem 1
• What is the magnitude and
direction of the electric field 30.0
cm directly above a 33.0 x 10-6 C
charge?
Sample Problem 1
• What is the magnitude and direction of the electric
field 30.0 cm directly above a 33.0 x 10-6 C charge?
• Now, we're into point charges. In the info given, we have
a radius (distance between charge and point charge), as
well as 1 Charge (33e-6 C).
• E = kq/r2
• E = (8.988e9)(33e-6)/(.3)2
• E = 3.29e6 Up
• Because this charge is positive, the electric field is
always away from the charge. If the point is directly
above the charge, then the electric field will travel out to
the point, and past it... up.
Sample Problem 2 example 16-8 page 452
Two point charges are separated by the distance
of 10.0cm. One has a charge of -25μC
(micrometer) and the other +50μC (micrometer).
a.) Determine the direction and the magnitude of
the electric field at point P between the two
charges that is 2.0 cm from the negative charge.
b.) If an electron (mass = 9.11 x 10 to -11 power
kg) is placed at the rest at P and then released,
what will be its initial acceleration (direction &
magnitude) ?
Sample Problem 2 example 16-8 page 452
Two point charges are separated by the distance of 10.0cm. One has a charge
of -25μC (micrometer) and the other +50μC (micrometer).
a.) Determine the direction and the magnitude of the electric field at point P
between the two charges that is 2.0 cm from the negative charge.
Sample Problem 2 example 16-8 page 452
b.) If an electron (mass = 9.11 x 10 to -11 power kg) is placed at the rest at P
and then released, what will be its initial acceleration (direction & magnitude) ?
The force on the electron = qE
= 1.6x10-19 x 6.33x108
= 1.01x10-10 N
Because the electron is negative, the direction is opposite to
the field's direction (away from the negative charge and
towards the positive charge). It will feel a force to the right.
Since F=ma, a = F/m
a = 1.01x10-10 / (9.11x10-31)
= 1.11x1020 m/s²
The direction is the same as the force, away from the
negative charge and towards the positive charge which will
be to the right.
16.8 Field Lines
The electric field can be represented by field
lines. These lines start on a positive charge
and end on a negative charge.
16.8 Field Lines
The number of field lines starting (ending)
on a positive (negative) charge is
proportional to the magnitude of the charge.
The electric field is stronger where the field
lines are closer together.
16.8 Field Lines
Electric dipole: two equal charges, opposite in
sign:
Electric Field Lines—
Physical Meaning
Electric Field Lines—Examples
Beginning with positive charge and ending at negative or infinity
Drawing the electric field
Electric fields and electric force
On the Earth’s surface, the gravitational field creates 9.8 N
of force on each kilogram of mass.
With gravity, the strength of the field is in newtons per
kilogram (N/kg) because the field describes the amount
of force per kilogram of mass.
Electric fields and electric force
With the electric field, the strength is in newtons per
coulomb (N/C).
The electric field describes the amount of force per
coulomb of charge.
16.8 Field Lines
The electric field between
two closely spaced,
oppositely charged parallel
plates is constant.
Capacitors
• A capacitor is a storage device for electric
charge.
 Capacitors can be connected in series or
parallel in circuits, just like resistors.
Capacitors
• A capacitor can be charged by connecting it to a battery
or any other source of current.
• A capacitor can be discharged by connecting it to any
closed circuit that allows current to flow.
How a capacitor works inside
• The simplest type of
capacitor is called a parallel
plate capacitor.
• It is made of two conductive
metal plates that are close
together, with an insulating
plate in between to keep the
charges from coming
together.
• Wires conduct charges
coming in and out of the
capacitor.
How a capacitor works inside
The amount of charge a capacitor can store
depends on several factors:
1. The voltage applied to the capacitor.
2. The insulating ability of the material between
the positive and negative plates.
3. The area of the two plates (larger areas can
hold more charge).
4. The separation distance between the plates.
Electric Field Lines—Examples
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How Capacitors Store Electrical Energy
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16.8 Field Lines
Summary of field lines:
1. Field lines indicate the direction of the
field; the field is tangent to the line.
2. The magnitude of the field is proportional
to the density of the lines.
3. Field lines start on positive charges and
end on negative charges; the number is
proportional to the magnitude of the
charge.
16.9 Electric Fields and Conductors
The static electric field inside a conductor is
zero – if it were not, the charges would move.
The net charge on a conductor is on its
surface.
16.9 Electric Fields and Conductors
The electric field is
perpendicular to the
surface of a conductor –
again, if it were not,
charges would move.
phET Point charges in Electrostatic fields
Homework
• Page 466
• Problems 32 and 35
• Electric Field lines hand-out