Download 2. Electric field and electric potential (including point charges)

GUIDED NOTES
Unit 10: Electricity and Magnetism – Electrostatics
OBJECTIVES:1
II. Electricity and Magnetism
A. Electromagnetism
1. Charge and Coulomb’s Law:
a. Students should understand the concept of electric charge so they can:
1. Describe the types of charge and the attraction and repulsion of charges.
2. Describe polarization and induced charges.
b. Students should understand Coulomb’s Law and the principle of superposition so they
can:
1. Calculate the magnitude and direction of the force on a positive or negative charge
due to other specified point charges.
2. Analyze the motion of a particle of specified charge and mass under the influence of
an electrostatic force.
2. Electric field and electric potential (including point charges)
a. Students should understand the concept of electric field so they can:
1.) Define it in terms of the force on a test charge.
2.) Describe and calculate the electric field of a single point charge.
3.) Calculate the magnitude and direction of the electric field produced by two or more
point charges.
4.) Calculate the magnitude and direction of the force on a positive or negative charge
placed in a specified field.
5.) Interpret an electric field diagram.
6.) Analyze the motion of a particle of specified charge and mass in a uniform electric
field.
b. Students should understand the concept of electric potential so they can:
1.) Determine the electric potential in the vicinity of one or more point charges.
2.) Calculate the electrical work done on a charge or use conservation of energy to
determine the speed of a charge that moves through a specified potential difference.
3.) Determine the direction and approximate magnitude of the electric field at various
positions given a sketch of equipotentials.
4.) Calculate the potential difference between two points in a uniform electric field and
state which point is at the higher potential.
5.) Calculate how much work is required to move a test charge from one location to
another in the field of fixed point charges.
6.) Calculate the electrostatic potential energy of a system of two or more point charges
and calculate how much work is required to establish the charge system.
B. Conductors and Capacitors (and Dielectrics)
1. Electrostatics with conductors
a. Students should understand the nature of electric fields in and around conductors so they
can:
1
These are the outlined objectives of the AP Physics B course as laid out by the College Board. We will continue to
build this outline throughout the year. We do not do all of the objectives listed in the AP outline, as some are only
for AP Physics C. Therefore missing numbers or letters is intentional.
GUIDED NOTES
1.) Explain the mechanics responsible for the absence of electric field inside a conductor
and know that all excess charge must reside on the surface of the conductor.
2.) Explain why a conductor must be an equipotential and apply this principle in
analyzing what happens when conductors are connected by wires.
b. Students should be able to sketch a graph of the electric field and potential inside and
outside a charged conducting sphere.
c. Students should understand induced charge and electrostatic shielding so they can:
1.) Describe the process of charging by induction.
2.) Explain why a neutral conductor is attracted to a charged object.
2. Capacitors
a. Students should understand the definition and function of capacitance so they can:
1. Relate stored charge and voltage for a capacitor.
2.) Relate voltage, charge, and stored energy for a capacitor.
3.) Recognize situations in which energy stored in a capacitor is converted to other
forms.
b. Students should understand the physics of the parallel-plate capacitor so they can:
1.) Describe the electric field inside the capacitor and relate the strength of this field to
the potential difference between the plates and the plate separation.
3.) Determine how changes in dimension will affect the value of the capacitance.
NOTES:
I. Charge and Coulomb’s Law
A. Charge
1. Charge is a ______________ of particles that ______________________________ of other
charged particles.
a. Symbol:
b. Unit:
c. Two types of charged particles:
1.) Electrons:

𝑞 =

mass =
2.) Protons:

𝑞 =

mass =
3.) Neutrons are _______________ with a mass equal to a _____________ mass.
d. Charge is _______________, and ___ is the ________________________________.
1.) Magnitude of elementary charge: 𝑒 = ___________________(An electron’s
charge is the negative of this magnitude, and a proton the positive.)
GUIDED NOTES
2.) Quantized charge: No object can have a fraction of an electron or proton, so all
charged objects are whole-number multiples of 𝑒. That means charge is quantized, and
all objects have a charge equal to N 𝑒.
e. Rule of Charges: Like charges repel, opposite charges attract.
f. Law of Conservation of Charge: Charge can neither be created nor destroyed but can
transfer.
2. Ways to be charged
a. Excess of one type of particle due to ______________ from one object to another
1.) Negatively-charged: More electrons than protons due to having _________________
2.) Positively-charged: More protons than electrons due to having _________________
b. _____________________
1.) A neutral conductor has the ability to transfer charge from one side of itself to the
other when exposed to but not touched by a charged object. The charged object is then
attracted to the induced object. If the induced object is grounded, it can hold the
charge.
2.) Sketch of the process
c.) _____________________
1.) A neutral insulator has the ability to transfer electrons to one side of each molecule
but not throughout the entire object when exposed to but not touched by a charged
object. The charged object is then attracted to the polarized object.
2.) Sketch of the process
GUIDED NOTES
B. Coulomb’s Law describes the _________________________ between two or more charges
1. Formula:

𝑘 is ___________________
o
𝑘=

_____ is the ______________________________ (the ability of a
vacuum to permit electric force field lines) This is a constant on the
front page of your formula sheet.

∈0 =
o
𝑞1 and 𝑞2 are the ______________ of the two charges
o
𝑟 is the _____________ between the charges
2. Example 1: Find the net electrostatic force on 𝑞3 . (Start by simply stating how to solve it.)
3. Example 2: Find the acceleration of the particle.
GUIDED NOTES
II. Electric field and electric potential
A. ________________________
1. The ___________ of an __________________ on _____________________ at a
______________________________
2. 𝐸 =

𝐹 is the _____________________________

𝑞0 is the ____________________________
o
A test charge is a particle whose charge is so __________ that it does not
affect the field.

SI Unit:

A _________________
3. Also, not on formula sheet: 𝐸 = __________ for the field created by a charge.
4. Example 3: Two point charges are separated by a distance of 10.0 cm. One has a charge of
-25µC and the other +50 µC. (a) What is the direction and magnitude of the electric field at a
point P in between them, that is 2.0cm from the negative charge? (b) If an electron is placed at
rest at P, what will its acceleration be initially?
5. __________________________
a. Used to model an electric field
b. Rules for drawing:
1.) Lines point in the direction a _______ test charge would move, ______________
__________________________ and _______________________________________.
2.) The _____________________ is proportional to the field __________ at a location.
GUIDED NOTES
c. Examples:
1.) Two positive equal charges
2.) Two negative equal charges
3.) Two charges, uneven strength
4.) Parallel plates
5.) Parallel plates with a charge in the middle
GUIDED NOTES
6.) Spherical shell, in and out
B. ______________________________ (a.k.a. ______________)
1. ___________________________________
a. Charged particles in an electric field have electric potential energy.
b. Formula:

_____ is the electric potential energy in the charge

_____ is the point charge with the energy

_____ is the electric potential (next topic…)
2. __________________________
a. Basics:
1.) The _______ of _________________________________of charge that a point charge
has at a particular location in an electric field
2.) Formula relating to energy and charge:

_____ is the point charge with the energy.

_____ is the electric potential.

_____ is the distance from the source of the electric field.
o
In a battery, we look at positive charges having a potential to move toward
the negative terminal. The electric potential at the positive end is 1.5V.
Along the way, the electric potential decreases to 0V at the negative end.
GUIDED NOTES
3.) Formula relating potential to electric field:

_____ is the electric field strength.

_____ is the distance from the source of the field.

On the formula sheet, this is written in terms of 𝐸𝑎𝑣𝑔 = − 𝑑
𝑉
4.) Units: _____________ where ______________

_____________________
o
An _____________________ is the amount the _______________________
of _________________ changes when moving through a potential
difference of _________.
o
_________________________________
5.) Electric potential is a ____________.
6.) Other names for electric potential: ____________________________
b. Potential of Point Charges
1.) In addition to having potential due to being in an electric field, each charge can also
alter the potential in its region according to ____________________
o
In this case, we are looking at how much the electric potential there is
around that point charge at a location 𝑟, which is different from how much
potential a point charge has in an electric field. Same equation, slightly
different concept
2.) A series of point charges can alter the potential in their region according to the sums
of each one’s influence according to ________________________________________
3.) Example 4: An electron and a proton are 5.3E-11 m apart in a hydrogen atom. What
is the potential mid-way between them? What is the potential at the position of the
electron?
GUIDED NOTES
4.) Example 5: Four charges are placed on the corners of a square. The charges are
+1 𝜇C, -2 𝜇C, +3 𝜇C, and -4 𝜇C moving clockwise from the top left. What is the voltage in
the center if the length of the square’s sides is 1m.
3. ____________________: The difference in electric potential from one position to another, 𝛥𝑉
4. Work and potential
a. Work must be done to increase the electric potential energy of a charge, and work equals
change in kinetic energy.

This changes 𝑟, so it changes 𝐹 and 𝐸. Therefore Calculus is needed.

For us, ___________________________________
relating the work to move the charge from position A to position B (not on formula
sheet)
b. Direction of motion…by convention…

A __________ charge __________ a region of _______________to _____________.

A negative charge moves from a region of low potential to high potential.

Sketches
o
Between two charged plates
o
Simple circuit (work done by battery by using its chemical potential energy;
appliance uses the energy to function)
GUIDED NOTES
c. Examples:
1. Example 6: A proton is released from rest at a point with 200V and moves to a point
with 50V. Find (a) the final velocity of the ion and (b) the work required to move the ion
back to its original position. Express your answer in both Joules and electron volts.
2. Example 7: Two parallel plates connected to a 50V power supply are used to
accelerate electrons from rest. (A) If electrons accelerate from A to B, which plate has
higher V? (b) Find ΔK in eV and J for an electron. (c) Find the speed of the electron when
it emerges from plate B.
5. _____________________________
a. Equipotential lines mark surfaces along _______________________________, similar to
contour lines on a map.
1.) They ___________________________ at _______________.
2.) To move up in voltage takes work. To move down turns UE into K. To move along the
lines takes ________________ and does not change the object’s energy.
GUIDED NOTES
b. Example 8: Given the equipotential lines below (a) draw the direction of the electric field
at points A, B, and C. (b) Rank the electric field strength at A, B, and C from high to low. (c)
Estimate the magnitude of the electric field at point B.
III. Electrostatics with Conductors
A. Conductors readily allow __________________.
B. Charge distribution
1. Excess charge migrates to ____________________________________ due to electrostatic
____________________ of like charges.
2. ______________________________: The electric field is __________ __________ of a
conductor because the even distribution of charge along the surface __________ out an electric
field within the object.
a. Example: Faraday cages
b. Decent animation: http://www.youtube.com/watch?v=yHfgqDcEqfA
3. Therefore the _______________________________constitutes an ____________________.
4. Example 9: Sketch the electric field and equipotential lines around and within a charged
spherical object.
GUIDED NOTES
C. ____________________
1. Structure
a. ______ conductors, ____________________charged and ___________________charged,
are placed ________ each other but are separated by an __________material called a
____________________.
b. Sketches
2. ____________________
a. The ______________________________when a capacitor is connected to an __________
voltage source, ________________________________________within the capacitor.
b. Symbol:
c. SI Unit:
d. Formula:
1.)

_______is the charge on each plate

_______is the potential difference between the plates

_______ is the permittivity of free space (vacuum permittivity)

_______ is the surface area of each conductor

_______ is the distance between the conductors
2.)
e. Energy storage
1.) Capacitors store electric energy.
2.) Formula:
f. Example 10: A camera flash unit stores energy in a 150𝜇F capacitor at 200V. How much
electric energy can be stored? What is the power output if the flash releases the energy in
0.001 seconds?