Download Electrostatics I

Electrostatics I
Introduction
Textbook Readings: Ch. 20, Static Electricity
I. Introduction: The types of forces studied so far have involved some type of contact or were attracted to
one another by gravity. List some everyday experiences that do not fall into the above interactions:
Definition: Static electricity means . . . . . . .
II. Historical Development:
When certain materials are rubbed together, something is exchanged between
the materials. This something is referred to as ________________ .
Originally, charge was seen as a fluid that could be transferred from one
substance to another. When one substance accepts this fluid, it becomes
positively charged, while the other that gave up the fluid becomes
negatively charged. The idea of positive and negative charge is credited
to _________________ ________________ .
Franklin deduced two types of opposite charges based on the
forces of attraction and repulsion that form when two charges
are brought near one another.
Like charges ___________________ .
Opposite charges ___________________ .
Ex. #1: Based on this information, determine the directions
of the unmarked forces in the diagram below.
III. Chemistry Review:
A. Structure of matter, types of charge:
B. What are atoms composed of?
C. Distribution in atom?
D. Atoms with the number of ___________ and ____________ equal are said to be neutral.
E. How are atoms charged?
F. The ease with which ____________ transfer or move depends on how tightly they are held.
G. How are macroscopic objects (objects made up of many atoms) charged?
H. If the # of electrons > # of protons, atom (or object) has a ____________ charge.
If the # of electrons < # of protons, atom (or object) has a ____________ charge.
IV. Units of Charge:
The basic unit of charge is called the ______________, and it is represented by the letter ___.
This unit is its own Fundamental unit. From chemistry, another useful charge is that of the electron and
proton. This charge, known as the Fundamental charge, is:
V. Conductors & Insulators
A. A conducting material allows for the easy transport of
___________ throughout the medium. Electrons may also be lost
from the ___________ of the medium.
B. An insulating material keeps its electrons ___________
bound, even in the presence of a net charge on the material.
VI. Transfer or Motion of Charges:
A. Conduction: If a charged object comes in direct contact with an uncharged object, the charge
will ______________ itself throughout both objects. When the objects are separated, the bodies will
____________ their charges. The new charge is:
Ex. #2: A charge of +14.0 C comes in contact with a charge of –25.0 C.
What is the charge on each object after conduction of charge occurs?
B. Induction: If a charged object is brought near, but not touching, an uncharged object, the
uncharged object will experience a net charge separation. When the charged object is removed, the object
with the net charge separation will ____________ its charge separation.
More charging by induction diagrams:
Electrostatics II
Forces and The Inverse Square Law
Homework #1: End of this packet.
As with any force, at least ___________ objects must be present: one object ______________ a force on
the other object, and by Newton's _____________ law, that other object exerts an ______________ but
_______________ force on the first.
I. Electrostatic Force Between Two Charges:
The force of attraction or repulsion between two charges behaves the
same as the gravitational force. The force will be proportional to the charges,
q1 and q2, and inversely proportional to the distance between the centers of the
objects (r).
The charge q of any object is measured in Coulombs, the basic unit
of charge. Like mass, distance, and time, charge is a fundamental unit. The
magnitude of the charge on a proton or an electron is 1.6022 x 10 –19 C.
The magnitude of the force is given by the following:
The constant k has the value 8.988 x 109 Nm2/C2 . The direction of the force is based on the actual value
of the charges: if both charges are either positive or negative, the force is ______________ and directed
away from the other charge; if, on the other hand, the two charges have opposite signs, then it is an
_____________ force.
Example #1: Two charges are placed on the x-axis as follows: A charge of +1.25 C is placed at the
origin and a charge of –34.2 C is placed at the 14.0 cm mark. a. What is the force between the two
charges, given in magnitude and direction?
b. The two charges are briefly connected by a conducting wire. What will happen to the force now?
Example #2: Two identical charges are placed 16.0 cm apart and exert a force of 0.128 N on one another.
What is the amount of charge on each object?
Example #3: For the hydrogen atom, the proton and the electron are approximately 0.50 Å apart. Compare
the size of the electric force between the charges and the gravitational force between the masses. Which is
more important to the structure of the hydrogen atom?
II. Electric Force Between Multiple Charges:
When calculating the force on a charge, q, by several other charges, Qi, compute the force on the
charge q pair wise for each other charge. The total force is the vector sum of all the forces from the other
charges. Below is a sample image showing three interacting charges. The diagram shows the forces acting
on the charge Q3 at the upper left corner. Describe the results of the image:
Example #4: Three charges are placed on the x-axis: Q1 = +3.50 C is placed at x = 0, Q2 = +4.40 C is
placed at x = 3 cm, and Q3 = –8.40 C is placed at x = 7.00 cm. a. Find the total force on the charge Q 2.
b. If the charge Q2 has a mass of 275 grams, what would be its acceleration at that moment?
c. Determine the magnitude and direction of the net force acting on the charge Q1.
Example #5: Two charges are placed on the x-axis: Q1 = +16.0 C is placed at x = 0 and Q2 = +144 C is
placed at x = 9.00 cm. Where should a charge, q, be placed so that the total force on q is zero?
Example #6: Three charges are placed on the x,y coordinate system. A charge Q1 = +17.0 C sits at (x,y)
of (0,+3.00 m), a charge Q2 = +95.0 C sits at the origin, and a charge Q3 = –23.0 C sits at (4.00 m,0).
What is the force on the charge Q2?
Example #7: In a simple model of the hydrogen atom, the electron revolves in a circular orbit around the
proton with a speed of 1.1 x 106 m/s. Determine the radius of the electron’s orbit.
Example #8: Determine the value of the quantity Q if each mass below is 24.0 grams and the system is in
equilibrium.
Ex. #9: Two charges are placed 80.0 cm apart. The sum of the two charges is 100 C and the two charges
exert a repulsive force of 32.0 N on one another. What is the size of each charge?
Ex. #10: Solve the net force on the charge Q3.
Electric Field: Day #1
Introduction:
When scientists try to study an unknown arrangement of charges, the
only tool available is to place a test charge near the distribution and measure
the force on the test charge. The downside to this technique is that the test
charge might cause a change to the distribution of charge.
The electric field is a mathematical tool used by physicists to represent the
strength of electric forces available at a given location without the physical interaction of
a real charge at that location.
An imaginary positive test charge, q, is placed at some location near a
distribution of charge. A force F would be exerted on this test charge. The electric
field measures the force available at that point in space, but represents it as the
force per unit charge. In other words:
F
Units:
E  lim
q 0 q
The electric field can then be mapped around some given charge
distribution (without altering the charge distribution due to measurements).
Direction of Electric Field:
Forces Caused by Electric Fields: The force on any charged particle, q,
that is placed into an electric field, is given as:
If q > 0, the force is in the same direction as the electric field. If q < 0, then the force on
the charge points opposite of the electric field.
Point Charges as Sources of Electric Fields:
The electric field created by a point charge (or spherical distribution of charge)
will point radially outwards from or inwards towards the charge. Imagine the direction of
the force exerted on some test charge that is placed near the source charge.
The strength of the electric field for a point (Figure 6 above) charge is given as follows:
Electric Field: Day #2


Force on a test charge: F  qE {always true}
kQ
Electric field for a point source charge: E  2
r
1. A point charge with a mass of 1.40 kg and charge of +25.0 mC is placed into a
constant electric field. a. If the strength of the electric field is 863 N/C pointing due
north, what is the force on the charged particle?
b. If the particle starts from rest, how long will it take the particle to reach 15.0 m/s?
2. An object with a net charge of 24 μC is placed in a uniform electric field of 610 N/C,
directed vertically. What is the mass of the object if it “floats” in the electric field?
3. An electron is accelerated by a constant electric field of magnitude 300 N/C. (a) Find
the acceleration of the electron. (b) Use the equations of motion with constant
acceleration to find the electron’s speed after 1.00 × 10−8 s, assuming it starts from rest.
4. An airplane is flying through a thundercloud at a height of 2000 m. (This is a very
dangerous thing to do because of updrafts, turbulence, and the possibility of electric
discharge.) If there are charge concentrations of +40.0 C at a height of 3000 m within the

cloud and −40.0 C at a height of 1000 m, what is the electric field E at the aircraft?
5. A proton accelerates from rest in a uniform electric field of 640 N/C. At some later
time, its speed is 1.20 × 106 m/s. (a) Find the magnitude of the acceleration of the proton.
(b) How long does it take the proton to reach this speed?
(c) How far has it moved in that interval?
(d) What is its kinetic energy at the later time?
6. Each of the protons in a particle beam has a kinetic energy of 3.25 × 10−15 J. What are
the magnitude and direction of the electric field that will stop these protons in a distance
of 1.25 m?
7. Each of the electrons in a particle beam has a kinetic energy of 1.60 × 10−17 J. (a)
What is the magnitude of the uniform electric field (pointing in the direction of the
electrons’ movement) that will stop these electrons in a distance of 10.0 cm? (b) How
long will it take to stop the electrons? (c) After the electrons stop, what will they do?
Explain.
8. Three identical charges (q = −5.0 μC) lie along a circle
of radius 2.0 m at angles of 30°, 150°, and 270°, as shown
in the figure at right. What is the resultant electric field
at the center of the circle?
9. (a) Determine the electric field strength at a point 1.00 cm to the left of the middle
charge shown in the figure below. (b) If a charge of −2.00 μC is placed at this point, what
are the magnitude and direction of the force on it?
10. Three point charges are aligned along the x-axis as shown in the figure below. Find
the electric field at the position x = +2.0 m, y = 0.
11. A small 2.00-g plastic ball is suspended by a 20.0-cm-long string in a uniform
electric field, as shown in the figure below. If the ball is in equilibrium when the string
makes a 15.0° angle with the vertical as indicated, what is the net charge on the ball?
12. A positively charged bead having a mass of 1.00 g falls from rest in a vacuum from a
height of 5.00 m in a uniform vertical electric field with a magnitude of 1.00 × 104 N/C.
The bead hits the ground at a speed of 21.0 m/s. Determine (a) the direction of the
electric field (upward or downward), and (b) the charge on the bead.
Electric Potential 2014:
Introduction:
So far, we have concentrated on the interactions of charges through the forces between charges. These
interactions can also be modeled through energy, which provides us an explanation of motion from a
different point of view. The concepts we will use are:
Whenever there is a force between two objects, or between an object and a force field, energy can be stored
in this interaction. Energy is the ability of an object to perform work. When an object moves under the
actions of a force, work is done. For certain forces, this work can be related to stored energy, called
potential energy.
The electric field relates the amount of force available at some location in space, even if there is no charge
in that location to feel the force. Similarly Earth’s gravitational field relates the amount of force that could
be exerted on some object at a particular location, even if there is no object at that location. The electric
field is the force per unit charge available at a given point in space.
A similar definition can be made for energy. The electric potential is to potential energy what the electric
field is to force.
Units on various quantities…
Example #1: Show that the units of electric field can also be written as volts per meter.
Derivation of Electric Potential for a Constant Electric Field:
It is instructive to see how electric potential is defined and how it relates to the movement of charges in an
electric field. Although this is derived for constant electric fields, it generalizes to more complicated
arrangements of fields and charges. You will not be required to derive all of this again on homework or on
the exam. You are expected to understand the fundamental concepts.
Start by placing a charge q into an electric field and note the direction of the force on the charge:
Next consider moving this charge through the electric field. The force on the charge by the electric field
will do work on the charge q.
Now substitute in specifically the force on a charge in an electric field:
Since the electric field is a conservative force, a potential energy can be defined for it:
Now define the change in electric potential as the change of potential energy per unit of charge:
Major Concepts:
For the three equations given (work, potential energy, and electric potential), there are three primary cases
to know and understand. The three cases are primarily motion at angles of 0º, 90º, and 180º.
Case I: 90º
An angle of 90º indicates motion perpendicular to the electric field. All three concepts depend on the
cosine of 90°, which has a value of zero.
Case II: 0º
This is motion in the same direction as the electric field. The change of electric potential is independent of
the charge moving in the electric field, and the value of this is given as follows:
Motion in the direction of the electric field lowers the electric potential. The electric field always
points from high electric potential to low electric potential.
Case II: 0º {continued}
If a charged particle moves in the direction of the electric field:
When a positive charge moves in the direction of the electric field, the field does positive work on the
charge. The charge also lowers its potential energy.
The opposite holds true for a negative charge moving in the direction of an electric field: work on
the charge by the field is negative and the particle gains potential energy.
Case III: 180º
This is motion in the opposite direction as the electric field. The change of electric potential is independent
of the charge moving in the electric field, and the value of this is given as follows:
Motion opposite to the direction of the electric field raises the electric potential. Again, the electric
field always points from high electric potential to low electric potential.
Case III: 180º {continued}
If a charged particle moves opposite to the direction of the electric field:
When a positive charge moves opposite to the direction of the electric field, the field does negative
work on the charge. The charge also gains potential energy.
The opposite holds true for a negative charge moving opposite to the direction of an electric field:
work on the charge by the field is positive and the particle loses potential energy.
Electric Potential 2012:
Review: Constant Electric Field
PE  q Ed ,
V 
PE
q
 Ed

1. For any motion perpendicular to an electric field E , the electric potential V and
potential energy PE do not change. No work is done by the electric field.
2. For any motion in the same direction as the electric field, the electric potential
decreases. For a positive charge, the potential energy of the charge will decrease. For a
negative charge, the potential energy will increase.
3. For any motion opposite to the direction as the electric field, the electric potential
increases. For a positive charge, the potential energy of the charge will increase. For a
negative charge, the potential energy will decrease.
Ex. #1: A proton moves 2.00 cm parallel to a uniform electric field of E = 200 N/C.
(a) How much work is done by the field on the proton?
(b) What change occurs in the potential energy of the proton?
(c) What potential difference did the proton move through?
Ex. #2: A potential difference of 90 mV exists between the inner and outer surfaces of a
cell membrane. The inner surface is negative relative to the outer surface. How much
work is required to eject a positive sodium ion (Na+) from the interior of the cell?
Ex. #3: An ion accelerated through a potential difference of 60.0 V has its potential
energy decreased by 1.92 × 10−17 J. Calculate the charge on the ion.
Ex. #4: The potential difference between the accelerating plates of a TV set is about 25
kV. If the distance between the plates is 1.5 cm, find the magnitude of the uniform
electric field in the region between the plates.
Ex. #5: Oppositely charged parallel plates are separated by 5.33 mm. A potential
difference of 600 V exists between the plates. (a) What is the magnitude of the electric
field between the plates?
(b) What is the magnitude of the force on an electron between the plates?
(c) How much work must be done on the electron to move it to the negative plate if it is
initially positioned 2.90 mm from the positive plate?
Electric Potential of a Point Charge:
Ex. #6: (a) Find the electric potential 1.00 cm from a proton.
(b) What is the electric potential difference between two points that are 1.00 cm and 2.00
cm from a proton?
Ex. #7: The three charges in the figure are at the vertices of an isosceles triangle.
Let q = 7.00 nC, and calculate the electric potential at the midpoint of the base.
Ex. #8: In Rutherford’s famous scattering experiments that led to the planetary model of
the atom, alpha particles (having charges of +2e and masses of 6.64 × 10−27 kg) were
fired toward a gold nucleus with charge +79e. An alpha particle, initially very far from
the gold nucleus, is fired at 2.00 × 107 m/s directly toward the nucleus, as in Figure
P16.19. How close does the alpha particle get to the gold nucleus before turning around?
Assume the gold nucleus remains stationary.
Capacitance
I. Define capacitance and a capacitor:
The simplest capacitor is one made of two ________________ metal sheets, or plates.
-Q
+Q
Q=
Note: Where there is a charge separation, there is also an
____________ field. The field exists between the
plates and points from _____ towards ____ .
Also, where there is an electric field, there is also an
___________ ___________ . The _____ plate is
the higher electric potential and the _____ plate is
the lower electric potential.
For a constant electric field, the change of electric potential is given by:
For the capacitor, this can be simplified to V  Ed . This is just the magnitude of the
electric potential between the two plates.
The capacitance is defined through the electric potential _____ and the charge held on the
plates, _____ . The equation for capacitance is:
Here
|V| =
Q=
C=
The units of capacitance are given the special name of ____________ and have a symbol
of ‘F’. What is the farad equivalent to?
Ex. 1: A parallel plate capacitor is made of circular metal sheets placed 0.100 mm apart
and has a capacitance of 1.00 F. If air is used as the insulator between the two metal
plates, what is the maximum amount of charge that may be stored on this capacitor? Air
ceases to be an insulator when the electric field is larger than 3 10 6 CN .
II. The capacitance of a parallel plate capacitor can be calculated from its dimensions:
The area of the overlap of the two sheets or plates and the distance between the plates.
A
A=
d=
d
So, C 
The capacitance, C, is proportional to the ________ and
inversely proportional to the _______________ between
the plates.
A
, or C =
d
The constant o is called the electric permittivity of free space, and the value of o is:
The permittivity constant is related to the coulomb constant, k  8.988  10 9
Nm 2
C2
. The
coulomb constant is derived from the force between charges, and the permittivity
constant is derived through Gauss’ Law. The actual relation is:
1
k
4o
Ex. 2: A 1.00 F capacitor is constructed with its metal plates set 0.100 mm apart. If the
plates are circular in shape, what is the diameter of the plates?
Ex. 3 A 1.00 F capacitor is constructed with square metal plates set 1.00 mm apart.
What is the length of a side for the metal plates?
III. Energy stored in a capacitor: Since the parallel plate capacitor has two plates that are
oppositely charged, there is energy stored in the electric interaction between the two
plates. This energy is stored in the electric field between the two plates. The energy is:
Q2
2
U  12 Q V  12 C V 
2C
Ex. 4: A parallel plate capacitor is made with an air gap of 0.0100 mm and circular plates
with a diameter of 3.25 cm. a. What is the capacitance of this capacitor?
b. What is the maximum charge that may be placed on this capacitor?
c. What is the energy stored in this capacitor?
d. What is the energy density between the plates of the capacitor?