Physics: Electrostatics
Massachusetts State Standards:
5. Electromagnetism
Central Concept: Stationary and moving charged particles result in the
phenomenon known as electricity and magnetism.
5.1
Recognize that an electric charge tends to be static on insulators and can move
on and in conductors. Explain that energy can produce a separation of charges.
5.4
Describe conceptually the attractive or repulsive forces between objects relative
to their charges and the distance between them (Coulomb’s law).
Essential Question:
1. How does electricity and magnetism allow us to use technology?
Guiding Questions:
1.
2.
3.
4.
5.
What is the magnitude and sign of the charge on an electron and proton?
How do you apply Coulomb's law?
What are insulators, conductors, and semiconductors?
What is an electric field?
How do you draw the electric field pattern and equipotential line pattern which exist
between charged objects?
6. What is the difference between electric potential, electric potential energy, and electric
potential difference?
7. How do you determine the magnitude of the potential at a point a known distance from a
point charge?
8. What is the relationship between electric potential and electric field?
I kind of know what this is, but
could not test well
I have a moderate grasp
of this concept
I know what this is and could test
well
I have a thorough understanding
and could teach this to another
2.
3.
4.
5.
UNIT: ELECTROSTATICS
(RATE YOUR UNDERSTANDING OF THE OBJECTIVES)
*For signatures, if the student attempts to explain a concept to you, but not thoroughly and not to a point
where you feel they understand it, initial NY for not yet. A NY will help a student identify areas of focus. Initial
when they describe the concept well enough for you to understand it as well.
1. Describe conditions for a net static charge on an object
2. Describe the charge, mass and relative mass of protons, neutrons and
electrons.
3. Describe the methods of charging by: conduction and induction
4. Describe how charge is generated on an object via the movement of
electrons
5. Differentiate between conductors and insulators.
6. Define and Differentiate between Electric Force, Electric Field, Electric
Potential and Electric Potential Energy.
7. Apply Coulomb's law to solve for the electrostatic force, charge values,
and the separation between the charges.
8. Determine electric fields due to charges and vice versa.
9. Sketch electric field lines and equipotential lines
10. Calculate work done by moving charges through an electric field
Preview: Electric charge is the fundamental quantity that underlies all electrical
phenomena. There are two types of charges, positive and negative, and like charges
repel each other, and unlike charges attract each other. A conductor is a material
through which charge can easily flow due to a large number of free electrons, whereas
an insulator does not allow charge to flow freely through it. The force between charges
can be found by applying Coulomb’s law. The electric field around a charge is the force
per unit charge exerted on another charge in its vicinity.
SIGNATURES/Initials
I have no idea
1.
PHYSICS CHART OF UNDERSTANDING
QUICK REFERENCE
Important Terms
capacitor
two oppositely charged conductors used to store charge and energy in an electric
field between them
charging by conduction
transfer of charge by actual contact between two objects
charging by induction
transfer of charge by bringing a charged object near a conductor, then grounding
the conductor
conservation of charge
law that states that the total charge in a system must remain constant during any process
coulomb
the unit for electric charge
Coulomb’s law
the electric force between two charges is proportional to the product of the charges and inversely proportional
to the square of the distance between them
electric charge
the fundamental quantity which underlies all electrical phenomena
electric field
the space around a charge in which another charge will experience a force; electric field lines always point from
positive charge to negative charge
electron
the smallest negatively charged particle
electrostatics
the study of electric charge, field, and potential at rest
electric potential
the amount of work per unit charge to move a charge from a very distant point to another point in an electric
field
electric potential difference
the difference in potential between two points in an electric field; also known as voltage
electric potential energy
the energy stored between two charges as a result of the electric force between them; also equal to the energy
needed to assemble two or more charges to a separation distance r.
equipotential surface
a surface which everywhere has the same potential
elementary charge
the smallest existing charge; the charge on one electron or one
proton (1.6 x 10-19 C)
parallel plate capacitor
capacitor consisting of two oppositely charged parallel plates of equal area, and
storing an electric field between the plates
proton
positively charged particle which can be found in the nucleus of an atom
neutral
having no net charge
Equations and Symbols
F
kq1 q 2
1 q1 q 2

4 0 r 2
r2
E
F kq
1 q
 2 
q0 r
4 0 r 2
EPE 
kq1 q 2
1 q1 q 2

r
4 0 r
V AB 
W AB EPE B  EPE A

q0
q0
Vr  
kq
1

r
4 0
q
r
Where:
F = electric force
k = electric constant = 9x109 Nm2 / C2
ε0 = permittivity constant
= 8.85 x 10-12 C2 / Nm2
q (or Q) = charge
r = distance between charges
E = electric field
EPE= electric potential energy
V=electric potential
Charges
Key Concept(s):
Conceptual Example 1-Positive electric charges:
a. attract both positive charges and negative charges.
b. repel both positive charges and negative charges.
c. attract positive charges and repel negative charges.
d. repel positive charges and attract negative charges.
Conceptual Example 2-Electric charge is:
a. caused by two fluids , as described by Benjamin Franklin.
b. present in metals only.
c. a fundamental property of matter that comes in two forms.
d. found only in non-living material.
Conceptual Example 3-An electric current will easily pass through
a. an absorber.
b. a conductor.
c. a semiconductor
d. an insulator.
Conceptual Example 4-Which of the following could be a good conductor of electricity?
a. A metal pot.
b. A ceramic coffee cup.
c. A piece of styrofoam packing material.
d. A plastic spoon.
Conceptual Example 5-Objects that conduct electricity poorly are called:
a. conductors.
b. insulators.
c. absorbers.
d. resistors.
Charge Transfer
Key Concept(s):
ConductionInductionCharge by frictionConceptual Example 1: An electroscope on the right is charged by bringing a negatively charged comb
close to the electroscope (but it does not touch the electroscope). The person next touches the
electroscope with a finger, then removes the finger, and finally removes the comb.
a. Is the electroscope positively or negatively charged? [A one-word
answer is acceptable here.]
b. What is this kind of charging process called? [A one-word answer
is acceptable here.]
c. Describe how the electroscope got its charge since the comb
never actually touched the electroscope. [Use complete
sentences.]
Conceptual Example 2:
In the chart below, draw representations of the objects with their charges for before and after
the balloon was rubbed on the cloth.
BALLOON
BEFORE
AFTER
CLOTH
Conceptual Example 3:
Now the balloon (from previous) is negatively charged and is able to stick to a wall. Illustrate
(via drawing) the charge distributions on the wall and the balloon:
Wall
Conceptual Example 3:
The diagrams below show two neutral, metal, conducting spheres which are placed on
insulating stands touching each other.
Step 1: A positively charged glass rod is brought near, but not touching, sphere A.
Step 2: Without moving the positively charged glass rod, the two metal spheres are pulled
apart, using their insulating stands as handles.
Step 3: The positively charged rod is removed.
Step 4: A positively charged piece of tape is brought near sphere B.
What happens to spheres A and B
when the charged glass rod is
brought nearby in Step 1? Explain.
Glass
rod
++
++
++
++
++
++
A
++
++
++
++
++
++
B
Glass
rod
Will the positively charged piece of
tape be attracted or repelled by
sphere B in step 4? Explain
Step 3
B
Step 2
Step 1
A
A
B
A
B
Step 4
++
++
++
++
Piece of
tape
Coulomb’s Law
Key Concept(s):
Example 1:
Three charged objects are put near each other in the picture below.
A
C
B
+4
+2
1 meter
-2
2 meters
a. How much bigger is the force between objects B and C than the force between objects B
and A? Show your work.
b. Which direction will each of the objects move? Why?
Example 2:
Draw the force vectors felt by the +1 charge, including a net force.
Example 3: (I) What is the repulsive electrical force between two protons 5.0 10 15 m apart
from each other in an atomic nucleus?
Example 4: (I) What is the magnitude of the force a 25 C charge exerts on a 3.0 mC charge
35 cm away?
Example 5: (II) Two charged spheres are 8.45 cm apart. They are moved, and the force on
each of them is found to have been tripled. How far apart are they now?
Example 6: (II) A charge of 6.00 mC is placed at each corner of a square 0.100 m on a side.
Determine the magnitude and direction of the force on each charge.
Electric Field
Key Concept(s):
Application Example 1:
(I) A proton is released in a uniform electric field, and it experiences an electric force of 3.75  10 14 N
toward the south. What are the magnitude and direction of the electric field?
Application Example 2:
(I) What are the magnitude and direction of the electric field 20.0 cm directly above an isolated
33.0 10 6 C charge?
Application Example 3:

(II) (a) Determine the electric field E at the origin due to the two charges at A and B.
Application Example 4:
(II) You are given two unknown point charges, Q1 and Q2 . At a point on the line joining them, one-third
of the way from Q1 to Q2 , the electric field is zero. What is the ratio Q1 Q2 ?
Electric Potential and Electric Potential Energy
Key Concept(s):
Conceptual Example 1:
Sketch the electric field lines and the equipotential lines around:
A: Two Point Charges
Conceptual Example 2:
State clearly the difference
(a) between electric potential and electric field
(b) between electric potential and electric potential energy.
Conceptual Example 3:
Can two equipotential lines cross? Explain.
B: parallel plates
Application Example 1:
(I) What is the electric potential 15.0 cm from a 4.00 C point charge?
Application Example 2:
(I) A point charge Q creates an electric potential of 125 V at a distance of 15 cm. What is Q?
Application Example 3:
(I) An electric field of 640 V m is desired between two parallel plates 11.0 mm apart. How large a
voltage should be applied?
Application Example 4 (I) How much work does the electric field do in moving a 7.7 C charge from
ground to a point whose potential is 55 V higher?
Multiple Choice Practice
1. A plastic rod is rubbed with a piece of wool. During the process the plastic rod acquires a positive
charge and the wool:
(A) acquires an equal positive charge
(B) acquires an equal negative charge
(C) acquires less in magnitude positive charge
(D) acquires less in magnitude negative charge
(E) remains neutral
2. A positively charged sphere is brought near one end of an uncharged metal bar. The end A and
B of the metal bar will be charged:
(A) positive, negative
(B) negative, positive
(C) positive, positive
(D) negative, negative
(E) neutral, neutral
3. Sphere A carries a net positive charge, and sphere B is neutral. They are placed near each other
on an insulated table. Sphere B is briefly touched with a wire that is grounded. Which statement
is correct?
(A) sphere B remains neutral
(B) sphere B is now positively charged
(C) sphere B is now negatively charged
(D) sphere B is now positive and sphere A is negative
(E) more information is required
4.
An originally neutral electroscope is briefly touched with a negatively charged plastic rod. Which
statement is correct?
(A) electroscope remains neutral
(B) electroscope becomes negatively charged
(C) electroscope becomes positively charged.
(D) electroscope becomes negatively charged and rod becomes positively charged
(E) electroscope becomes positively charged and rod remains negatively charged
Questions 5-6
5. An electric charge Q is placed at the origin. A charge q is placed at point B and the force on
charge q due to charge Q is F. What is the force on charge q if charge g is moved to point A?
(A) 4F
(B) 2F
(C) F
(D) F/2
(E) F/4
6. An electric charge Q is placed at the origin. A charge q is placed at point A and the force on
charge q due to charge Q is F. What is the force on charge q if charge g is moved to point C?
(A) 9F
(B) 3F
(C) F
(D) F/3
(E) F/9
7. A student in a physics lab wants to determine the type of an electric charge on initially charged
electroscope. He brings two charged rods without touching the electroscope. The positively
charged rod causes the leaves to move further apart and the negatively rod causes leaves to
move closer to each other. What type of the electric charge was initially on the electroscope?
(A) positive
(B) negative
(C) neutral
(D) couldn’t be determine because the electroscope wasn’t grounded
(E) couldn’t be determine because the electroscope wasn’t isolated
8.
Two charged objects with an equal charge of Q separated by a distance r attract each other with
a certain force. If the charges on both objects are doubled and the separation is halved, the force
between them is:
(A) 4 times greater
(C) 4 times less
(E) 16 times less
(B) 2 times greater
(D) 16 times greater
9. Two identical conducting spheres are charged to +Q and -3Q and separated by a distance r. The
attractive force between the spheres is F. The two spheres are brought in a brief contact and then
moved to the original positions. If the new electrostatic force between the spheres is F’, which of
the following is true?
(A) F’ = F
(B) F’ = 3F
(C) F’ = 1/3 F
(D) F’ = 9F
(E) F’ = 1/9 F
Questions 10-11
Three positive charges with an equal charge of Q are located at the corners of an equilateral
triangle of side r.
10. What is the direction of the net force on charge C due to charges A and B?
(A)
(B)
(C)
(D)
(E)
11. What is the magnitude of the net force on charge C due to two charges A and B?
Questions 12-13
Three equal in magnitude charges are located at the corners of an equilateral triangle of side r.
The charges A and C are positive and charge B is negative.
12. What is the direction of the net force on charge C due to charges A and B?
(A)
(B)
(C)
(D)
(E)
13. What is the magnitude of the net force on charge C due to charges A and B?
14. Four positive Q charges are arranged in the corner of a square as shown on the diagram. What is
the direction of the net force on the test charge q placed at the center of the square?
(A)
(B)
(C)
(D)
(E) the net force is zero
15. Four Q charges are arranged in the corner of a square as shown on the diagram. What is the
direction of the net force on the test charge q placed at the center of the square?
(A)
(B)
(C)
(D)
(E)
16. Four Q charges are arranged in the corner of a square as shown on the diagram. What is the
magnitude of the net force on the test charge q placed at the center of the square?
(A)
(B)
(C)
(D)
(E)
17. An electric charge Q is placed at the origin. If the magnitude of the electric field at point A is E,
what is the electric field at point B?
(A) 4E
(B) 2E
(C) E
(D) E/2
(E) E/4
18. A conducting sphere is charged with a negative charge –Q. Which statement about the charge
distribution is correct?
(A)
(B)
(C)
(D)
(E)
Charge is concentrated at the center of the sphere
Charge is concentrated at the bottom part of the sphere
Charge is evenly distributed throughout the volume of the sphere
Charge is evenly distributed on the surface of the sphere
More information is required
19. The conducting sphere shown above is charged with a negative charge –Q. Which statement
about the magnitude electric field of the sphere is correct?
(A) Maximum at the center
(D) Maximum at point 4 m
(B) Maximum at point 1 m
(E) Maximum at point 6 m
(C) Maximum at point 3 m
20. Two parallel conducting plates are charged with an equal and opposite charges. Which statement
is true about the direction of the electric field?
(A) Directed in +X (B) Directed +Y (C) Directed in -X (D) Directed in -Y (E) Directed –Z
21. Two parallel conducting plates are charged with an equal and opposite charges. Which statement
is true about the magnitude of the electric field?
(A) Greater at point A
(D) Greater at point D
(B) Greater at point B
(C) Greater at point C
(E) The same at points B, C, D and zero at point A
22. A conducting sphere with a radius R is placed in a uniform electric field produced by two parallel
plates M and L. Which statement is true about the electric field inside the sphere?
(A)
(B)
(C)
(D)
(E)
Increasing from the center to the surface
Decreasing from the center to the surface
Increasing from the left to the right across the sphere
Increasing from the bottom to the top across the sphere
Is zero everywhere inside the sphere
Questions 23-24
An electron with a charge e and mass m is accelerated from rest for a time T by a uniform electric
field that exerts a force F on the electron.
23. What is the magnitude of the electric field?
(A) eF
(B) F/m
(C) F/e
(D) em/F
(E) F/em
24. The speed of the electron after it has accelerated for the time T is most nearly
(A) eT/m
(B) FT/m
(C) emT/F
(D) FT/em
(E) m/FT
25. Two isolated charges, + 2q and -5q, are 2 centimeters apart. If F is the magnitude of the force
acting on charge -5Q, what are the magnitude and direction of the force acting on charge + 2q ?
Magnitude
(A)
(1/2) F
(B)
2F
(C)
F
(D)
F
(E)
2F
Direction
Toward charge -5q
Away from charge -5q
Toward charge -5q
Away from charge -5q
Toward charge -5q
26. Which of the following is true about the net force on an uncharged conducting sphere in a nonuniform electric field?
(A) It is zero
(B) It is in the direction of the field
(C) It is in the direction opposite to the field
(D) It produces a torque on the sphere about the direction of the field
(E) It causes the sphere to oscillate about an equilibrium position
27. Two negative charges A and B are placed at the corners of equilateral triangle. What is the
direction of the net electric field at point C?
(A)
(B)
(C)
(D)
(C)
28. Two negative charges A and B are placed at the corners of equilateral triangle. What is the
magnitude of the net electric field at point C?
(A)
(B)
Questions 29-30
(C)
(D)
(E)
The figure above shows two particles, each with a charge of -Q, that are located at the
opposite corners of a square of side d.
29. What is the direction of the net electric field at point P?
(A)
(B)
(C)
(D)
(C)
30. What is the net electric field at point P?
(A)
(B)
(C)
(D)
(E)
31. A point charge Q1 = +4.0 µC is placed at point -2 m. A second charge Q2 is placed at point +3 m.
The net electric field at the origin is zero. What is charge Q 2?
Magnitude
(A)
9.0 µC
(B)
6.0 µC
(C)
3.0 µC
(D)
6.0 µC
(E)
9.0 µC
Sign
(A) Positive
(B) Positive
(C) Positive
(D) Negative
(E) Negative
32. A small sphere with charge q and mass m is attached to one end of an insulating string of length
L. The other end is attached to negatively charged wall. The electric field E due to the charged
wall is constant in the vicinity of the charged sphere. The string makes a constant angle ϴ with
the vertical. What is the sign and magnitude of charge q?
(A) Positive and magnitude
(B) Positive and magnitude
(C) Negative and magnitude
(D) Negative and magnitude
(E) Negative and magnitude
33. A negative charge is placed on a conducting sphere. Which statement is true about the charge
distribution
(A)
(B)
(C)
(D)
(E)
Concentrated at the center of the sphere
Charge density increases from the center to the surface
Uniformly distributed on the sphere's outer surface.
Uniformly distributed inside the sphere
More information is required
34. An electric charge Q is placed at the origin. What is the ratio between the absolute potential at
point A and point B?
(A) 4/1
(B) 2/1
(C) 1
(D) 1/2
(E) ¼
35. Which of the following statements about conductors under electrostatic conditions is true?
(A) Positive work is required to move a positive charge over the surface of a conductor.
(B) Charge that is placed on the surface of a conductor always spreads evenly over the surface.
(C) The electric potential inside a conductor is always zero.
(D) The electric field at the surface of a conductor is tangent to the surface.
(E) The surface of a conductor is always an equipotential surface.
36. Which of the following represents the magnitude, of the potential V as function of r, the distance
from the center of a conducting sphere charged with a positive charge Q, when r > R?
(A)
(B)
(C)
(D)
(E)
0
kQ/R
kQ/r
2
kQ/R
2
kQ/r
37. Points A and B are each the same distance r from two
unequal charges, +Q and +2Q. The work required to
move a charge q from point A to point B is:
(A) dependent on the path taken from A to B
(B) directly proportional to the distance between A and B
(C) positive
(D) zero
(E) negative
38. An electric field is created by a positive charge. The distribution of the electric field lines and
equipotential lines is presented on the diagram. Which statement about electric potential is true?
(A)
(B)
(C)
(D)
(E)
VA > VB > VC > VD > VE
VA < VB < VC < VD < VE
VA = VD > VB > VC = VE
VA > VB = VC > VD = VE
VA > VB > VC = VD = VE
39. An electric field is created by a positive charge. The
distribution of the electric field lines and equipotential
lines is presented on the diagram. A test charge +q is
moved from point to point in the electric field. Which
statement about work done by the electric field on
charge +q is true?
(A) W A→B>W A→C
(B) W A→D>W A→E
(C) W D→C<W A→E
(D) W A→D=W C→E =0
(E) W A→B=W A→E
40. Two parallel conducting plates are charged with an equal and opposite charges. Which statement
is true about the magnitude of the electric potential?
(A) Greater at point A
(B) Greater at point B
(C) Greater at point C
(D) Greater at point D
(E) The same at points B, C, D and zero at point A
41. A point charge q is released from rest at point A and accelerates in a uniform electric field E.
What is the ratio between the work done by the field on the charge: W A→B/W B→C?
(A) 1/2
(B) 1/4
(C) 1
(D) 2/1
(E) 4/1
Answers for Multiple Choice:
1. B
2. B
3. C
4. B
5. A
6. E
7. A
8. D
9. C
10. B
11. A
12. C
13. E
14. E
15. E
16. B
17. E
18. D
19. C
20. D
21. E
22. E
23. C
24. B
25. C
26. B
27. D
28. B
29. C
30. A
31. E
32. C
33. C
34. B
35. E
36. C
37. D
38. C
39. D
40. B
41. C