Download An “electric field”

Physics B
Notes: Electrostatics
Name:___________________
The atom
Where is the positive charge in the atom? Is
it mobile?
Sample Problem
How much positive charge resides in two
moles of hydrogen gas (H2)?
Where is the negative charge in the atom?
Is it mobile?
How much negative charge?
Question
How can a negative balloon pick up a
neutral tissue?
How much net charge?
Sample Problem
The total charge of a system composed of
1800 particles, all of which are protons or
electrons, is 31x10-18 C.
How many protons are in the system?
Draw and label the electroscope
How many electrons are in the system?
Charge
What are the two types of charge?
Electric Force
What condition must exist for an electrical
force to be repulsive?
What is meant by the elementary charge?
What condition must exist for an electrical
force to be attractive?
Coulomb’s Law – form 1
Definition:
Sample Problem
A certain static discharge delivers -0.5
Coulombs of electrical charge. How many
electrons are in this discharge?
Equation:
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What condition must exist for Coulomb’s law
to hold?
Definition:
Sample Problem
Coulomb’s Law – form 2
Equation:
What is the force on the 4 C charge?
y (m)
2.0
1.0
Define the relationship between k and o.
-3 C
2 C
1.0
4 C
2.0
x (m)
Sample Problem
A point charge of positive 12.0 μC
experiences an attractive force of 51 mN
when it is placed 15 cm from another point
charge. What is the other charge?
Sample Problem
What is the force on the 4 C charge?
y (m)
2.0
-3 C
1.0
2 C
4 C
1.0
2.0
Sample Problem
Calculate the mass of ball B, which is
suspended in midair.
A
q = 1.50 nC
x (m)
R = 1.3 m
B
q = -0.50 nC
Superposition
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The Electric Field
An “electric field” is created in the space
around a charged particle or a configuration
of charges.
If a charged particle is placed in an electric
field created by other charges, it will
experience a force as a result of the field.
Sometimes we know about the electric field
without knowing much about the charge
configuration that created it.
We can easily calculate the electric force
from the electric field.
Field Vectors from Field Lines
Why use fields?
Force from Electric Field
Equation:
Field around + charge
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?
Field around - charge
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?
Field between charged plates
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Sample Problem
A proton traveling at 440 m/s in the +x
direction enters an an electric field of
magnitude 5400 N/C directed in the +y
direction. After 1.0 ms, find the velocity.
Draw the field around a pair of charges
Sample Problem
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?
For Spherical Electric Fields
Equation:
Does the Principle of Superposition apply to
Electric Fields?
Sample Problem
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?
Draw the field around an electric
dipole
Draw the field around a pair of +
charges
Sample Problem
What is the charge on the bead? It’s mass is 32 mg.
E = 5000 N/C
40o
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What conditions would produce high positive
electrical potential energy?
Excess Charges on Conductors
Where does the excess charge reside on a
charged conductor?
What conditions would produce low negative
electrical potential energy?
How does this help lightening rods to work?
How would you get zero electrical potential
energy?
Electric Field Inside a Conductor
Why is the field on the inside of an isolated
conductor necessarily zero?
Electric Potential
What do we commonly call electrical
potential?
Electrical Potential and Potential
Energy
Equation:
Draw an isolated conductor in an electric
field, and show how the charge is distributed
so as to nullify the external field.
Electrical Potential and Potential
Energy
Positive charges like to __________ their
potential (V ___ 0)
Negative charges like to ___________ their
potential. (V ___ 0)
Electric Potential Energy
Definition:
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Sample Problem
A 3.0 μC charge is moved through a
potential difference of 640 V. What is its
potential energy change?
Sample Problem
How much work would be done BY THE ELECTRIC FIELD in moving
a 2 mC charge from A to C? From A to B? from B to C?. How much
work would be done my an external force in each case?
y(m)
1.0
Electrical Potential in Uniform
Electric Fields
Equation:
Sample Problem
An electric field is parallel to the x-axis.
What is its magnitude and direction if the
potential difference between x =1.0 m and x
= 2.5 m is found to be +900 V?
C
A
B
1.0
2.0
x(m)
Conservation of Energy
You know what Conservation of Energy is.
We just need to work some problems.
Sample Problem
If a proton is accelerated through a potential
difference of 2.000 V, what is its change in
potential energy?
Sample Problem
What is the voltmeter reading between A and B? Between
A and C? Assume that the electric field has a magnitude
of 400 N/m.
y(m)
How fast will this proton be moving if it
started at rest?
C
1.0
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A
B
1.0
2.0
x(m)
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Sample Problem
A proton at rest is released in a uniform
electric field. What potential difference must
it move through in order to acquire a speed
of 0.20 c?
Electric Potential (spherical)
Formula:
Electric Potential Energy of
Spherical Charges
Equation:
Sample Problem
What is the electric potential at (2,2)?
y (m)
Sample Problem
What is the potential energy of the configuration shown below?
2.0
-3 C
1.0
2 C
4 C
1.0
2.0
y (m)
2.0
1.0
2 C
4 C
1.0
2.0
x (m)
x (m)
Equipotential surfaces: parallel
plate capacitor
Sample Problem
How much work was done in assembling the charge configuration
shown below?
y (m)
2.0
-3 C
1.0
2 C
4 C
1.0
2.0
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x (m)
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Equipotential surfaces: positive
point charge
Sample Problem
Draw a negative point charge of -Q and its
associated electric field. Draw 4
equipotential surfaces such that DV is the
same between the surfaces, and draw them
at the correct relative locations. What do you
observe about the spacing between the
equipotential surfaces?
Equipotential surfaces: negative
point charge
Question
What can you say about the intersection
between field lines and equipotential
surfaces?
Fill in the following table for
spherical charges
Force
Potential Energy
Field
Potential
Sample Problem
Draw field lines for the charge configuration below. The field is 600
V/m, and the plates are 2 m apart. Label each plate with its proper
potential, and draw and label 3 equipotential surfaces between the
plates. You may ignore edge effects.
- - - - - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -
++++++++++++++++++++++++++++++++
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Free Response Practice #1
A170B3. A small conducting sphere of mass 5 x 10 -3 kilogram, attached to a string of length 0.2 meter, is
at rest in a uniform electric field E, directed horizontally to the right as shown above. There is a charge of
5x10-6 coulomb on the sphere. The string makes an angle of 30° with the vertical. Assume g = 10 meters
per second squared.
a. In the space below, draw and label all the forces acting on the sphere.
b.
Calculate the tension in the string and the magnitude of the electric field.
c.
The string now breaks. Describe the subsequent motion of the sphere and sketch on the following
diagram the path of the sphere while in the electric field.
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Free Response Practice #2
A176B2. Object I, shown above, has a charge of + 3 x 10 -6 coulomb and a mass of 0.0025 kilogram.
a. What is the electric potential at point P, 0.30 meter from object I ?
Object II, of the same mass as object I, but having a charge of + 1 x 10 -6 coulomb, is brought from infinity
to point P, as shown above.
b. How much work must be done to bring the object II from infinity to point P ?
c.
What is the magnitude of the electric force between the two objects when they are 0.30 meter apart?
d.
What are the magnitude and direction of the electric field at the point midway between the two
objects?
The two objects are then released simultaneously and move apart due to the electric force between them.
No other forces act on the objects.
e. What is the speed of object I when the objects are very far apart?
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