MrHphysics

AP Physics 1: Electrostatics Enduring Understandings: Enduring Understanding 5.A: Certain quantities are conserved, in the sense that the changes of those quantities in a given system are always equal to the transfer of that quantity to or from the system by all possible interactions with other systems. Enduring Understanding 5.B: The energy of a system is conserved. Enduring Understanding 5.C: The electric charge of a system is conserved. Enduring Understanding 4.C: Interactions with other objects or systems can change the total energy of a system Enduring Understanding 3.G: Certain types of forces are considered fundamental. Enduring Understanding 3.B: Classically, the acceleration of an object interacting with other objects can be predicted by using Fnet = mass * acceleration Enduring Understanding 3.C: At the macroscopic level, forces can be categorized as either long–range (action–at–a–distance) forces or contact forces. Enduring Understanding 1.E: Materials have many macroscopic properties that result from the arrangement and interactions of the atoms and molecules that make up the material. Enduring Understanding 2.A: A field associates a value of some physical quantity with every point in space. Field models are useful for describing interactions that occur at a distance (long–range forces) as well as a variety of other physical phenomena. Enduring Understanding 1.B: Electric charge is a property of an object or system that affects its interactions with other objects or systems containing charge.

Essential Knowledge: Essential Knowledge 5.C.3: Kirchhoff’s junction rule describes the conservation of electric charge in electrical circuits. Since charge is conserved, current must be conserved at each junction in the circuit. Examples should include circuits that combine resistors in series and parallel. [Physics 1: covers circuits with resistors in series, with at most one parallel branch, one battery only. Essential Knowledge 3.C.2: Electric force results from the interaction of one object that has an electric charge with another object that has an electric charge.

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Essential Knowledge 3.B.1: If an object of interest interacts with several other objects, the net force is the vector sum of the individual forces. Essential Knowledge 3.B.2: Free–body diagrams are useful tools for visualizing forces being exerted on a single object and writing the equations that represent a physical situation. Essential Knowledge 1.E.2: Matter has a property called resistivity Essential Knowledge 2.A.1: A vector field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a vector Essential Knowledge 1.B.1: Electric charge is conserved. The net charge of a system is equal to the sum of the charges of all the objects in the system. Essential Knowledge 1.B.2: There are only two kinds of electric charge. Neutral objects or systems contain equal quantities of positive and negative charge, with the exception of some fundamental particles that have no electric charge. Essential Knowledge 1.B.3: The smallest observed unit of charge that can be isolated is the electron charge, also known as the elementary charge.

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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.

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(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.

SIGNATURES/Initials

I have no idea

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AP PHYSICS 1 CHART OF UNDERSTANDING ELECTROSTATICS

Learning Objective (1.B.1.1): Make claims about natural phenomena based on conservation of electric charge. [LO 1.B.1.1, SP 6.4] Learning Objective (1.B.1.2): Make predictions, using the conservation of electric charge, about the sign and relative quantity of net charge of objects or systems after various charging processes, including conservation of charge in simple circuits. [LO 1.B.1.2, SP 6.4, SP 7.2] Learning Objective (1.B.2.1): Construct an explanation of the two-charge model of electric charge based on evidence produced through scientific practices. [LO 1.B.2.1, SP 6.2] Learning Objective (1.B.3.1): Challenge the claim that an electric charge smaller than the elementary charge has been isolated. [LO 1.B.3.1, SP 1.5, SP 6.1, SP 7.2] Learning Objective (3.C.2.1): Use Coulomb’s law qualitatively and quantitatively to make predictions about the interaction between two electric point charges (interactions between collections of electric point charges are not covered in Physics 1 and instead are restricted to Physics 2). [LO 3.C.2.1, SP 2.2, SP 6.4] Learning Objective (3.C.2.2): Connect the concepts of gravitational force and electric force to compare similarities and differences between the forces. [LO 3.C.2.2, SP 7.2] Learning Objective (5.A.2.1): Define open and closed systems for everyday situations and apply conservation concepts for energy, charge, and linear momentum to those situations. [SP 6.4, SP 7.2]

Preview: Electromagnetic interactions are governed by one of the four fundamental forces of nature. The electric components of force are responsible for attraction and repulsion of charged particles. These interactions have many parallels with gravitational interactions. Laws of conservation of energy and momentum as well as Newton’s Laws of motion apply to electric interactions. KEY WORDS/TERMS Read and study the list of terms in your chapter notes packets. Be able to provide a clear definition for each of the terms as well as the laws/concepts below: 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

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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 electrical analogue to mass. Charges can attract or repel other charges based on their magnitudes and separation. 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 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 stored energy due to the location and magnitude of a charge in an electric field electron the smallest negatively charged particle electrostatics the study of electric charge, field, and potential at rest elementary charge -19 the smallest existing charge; the charge on one electron or one proton (1.6 x 10 C) neutral having no net charge test charge the very small charge used to test the strength of an electric field

EQUATIONS The following equations are provided on the free response section of the AP Exam. Become familiar with each of these variables and equations by doing a little research. You may use your textbook, handouts, the internet or other reliable sources. In addition to using this formulas to solve problems, a successful AP student will be able to write thorough explanations of their meaning and use these relations as justifications for open response writings.

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Charge and Transfer Learning Objective (1.B.1.1): Make claims about natural phenomena based on conservation of electric charge. [LO 1.B.1.1, SP 6.4] Learning Objective (1.B.1.2): Make predictions, using the conservation of electric charge, about the sign and relative quantity of net charge of objects or systems after various charging processes, including conservation of charge in simple circuits. [LO 1.B.1.2, SP 6.4, SP 7.2] Learning Objective (1.B.3.1): Challenge the claim that an electric charge smaller than the elementary charge has been isolated. [LO 1.B.3.1, SP 1.5, SP 6.1, SP 7.2]

Key Concept(s): Elementary charge-

Conservation of electric charge-

Conduction-

Induction-

Charge by friction-

Example 1 (1.B.1.1): A conducting sphere of radius 2m carries a charge of +9C. A second conducting sphere of radius 1m is neutral. The two charges come into contact, but remain insulated from contacting anything else. a. Describe any transfer of elementary particles between the two spheres when they come into contact.

b.

They separate. Determine the charge on each sphere.

c.

Determine the final electric potential difference between the two spheres. Justify your answer

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Example 2 (1.B.1.1): A neutral balloon is charged by a neutral person (Bob) wearing a wool sweater by rubbing along their sleeve. The balloon obtains a charge of -4C in the process. Bob places the balloon on the wall and it stays there. Bob also “zaps” a friend nearby with an outstretched finger. Assuming no other conductive surfaces are in contact with either person. A) What are the final charges of each item object afterwards? Justify your answer Earth

_____

Bob

_____

Friend

_____

Balloon _____

B) Bob and his friend separate and each go for a long walk in the woods. The balloon remains on the wall for 4 hours before eventually falling to the ground. Determine a suitable realistic range of charges for each: Earth

_________________

Bob

_________________

Friend

_________________

Balloon _________________ *Justify your answer

Example 3 (1.B.1.2) * (may revisit after circuits) In a simple circuit current is split at a junction. Explain the “Junction Rule” using the definition of current and conservation of charge.

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Example 4 (1.B.1.2): An electroscope on the right is charged by bringing a negatively charged plastic rod 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 plastic rod. a. Is the electroscope positively or negatively charged?

b. What is this kind of charging process called?

c. Describe how the electroscope acquired its charge.

d. Describe the energy transfers (if any) that occurred during the charging process.

e. Account for the law of conservation of electric charge during the process where a neutral person touches a neutral electroscope and it acquires a charge. (5.A.2.1)

Example 5 (1.B.3.1): 4 independent lab assistants measure the charge of a piece of plastic. All use different instruments with different levels of precision. Determine which scientists may have a correct reading. Justify your answer. -19 -21 Scientist A measures: 4.0 x 10 C +/- 2x 10 C -19 -20 Scientist B measures: 3.6 x 10 C +/- 2x 10 C -19 -21 Scientist C measures: 4.1 x 10 C +/- 4x 10 C -19 -20 Scientist D measures: 4.4 x 10 C +/- 4x 10 C

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Coulomb’s Law Learning Objective (3.C.2.1): Use Coulomb’s law qualitatively and quantitatively to make predictions about the interaction between two electric point charges (interactions between collections of electric point charges are not covered in Physics 1 and instead are restricted to Physics 2). [LO 3.C.2.1, SP 2.2, SP 6.4] Learning Objective (3.C.2.2): Connect the concepts of gravitational force and electric force to compare similarities and differences between the forces. [LO 3.C.2.2, SP 7.2]

Key Concept(s):

Gravity vs. Electrostatic Concepts: GRAVITY

ELECTROSTATIC

Field

Force

Potential Energy

“Potential”

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Example 1: A charged sphere is a distance of 2m from a point-charge of like charge. Explain two possible conditions that would result in a reduction of the electrostatic force by a factor of ½

Example 2: Two small spheres have charges q and 3q. They are separated by a distance d. The force exerted on the 3q charge by the q charge is F. If the charge on each sphere is doubled and d is halved, determine the force on each charge in terms of F:

F(on 3q) =

F(on q) = Example 3: The strength of both gravitational force and electrostatic force is characterized by a 1/r2 relation. Why do you think it is 1/r2 ? Can you describe any other physical phenomena that adheres to a 1/r2 rule?

Example 4: Surface gravity, g is different for planets of different size and mass. Is there an electrostatic equivalent to “g”? Explain.

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Example 5: Two positive charges are separated by a distance d. One of the charges is moved a distance d upwards (at a right angle to the original segment d). A) Draw force vectors felt by both charges in their final position

B) Write an expression for the magnitude of each force in terms of Q and d.

C) During the moving process, was work done on the system or by the system? Justify your answer.

Example 6: Unknown charges Q1 and Q2 . are separated by a distance d. At a point on the line joining them, one-fourth of the way from Q1 to Q2 , the electric field is zero. What is the ratio Q1 Q2 ?

Chapter 18 Coulomb’s Law Example Problems: #9 (easy) #17 (medium) #23 (harder) 10 https://sites.google.com/site/mrhphysics/

Example 7: Two identical charged masses hang as shown below from a string of known length and known angle. Describe measurements and calculations necessary to determine the charge on each mass.

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Related AP Exam Free Response:

–6

1993B2. A charge Q1 = –1.6 x 10 coulomb is fixed on the x–axis at +4.0 –6 meters, and a charge Q2 = + 9 x 10 coulomb is fixed on the y–axis at +3.0 meters, as shown on the diagram. a.

i. Calculate the magnitude of the electric field E1 at the origin O due to charge Q1 ii. Calculate the magnitude of the electric field E2 at the origin O due to charge Q2. iii. On the axes below, draw and label vectors to show the electric fields E 1 and E2 due to each charge, and also indicate the resultant electric field E at the origin.

b. Calculate the electric potential V at the origin. –6

A charge Q3 = –4 x 10 coulomb is brought from a very distant point by an external force and placed at the origin. c. On the axes below, indicate the direction of the force on Q3 at the origin.

d. Calculate the work that had to be done by the external force to bring Q3 to the origin from the distant point.

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2006Bb3. Three electric charges are arranged on an x–y coordinate system, as shown above. Express all algebraic answers to the following parts in terms of Q, q, x, d, and fundamental constants. a.

On the diagram, draw vectors representing the forces F 1 and F2 exerted on the +q charge by the +Q and –Q charges, respectively.

b.

Determine the magnitude and direction of the total electric force on the +q charge.

c.

Determine the electric field (magnitude and direction) at the position of the +q charge due to the other two charges.

d.

Calculate the electric potential at the position of the +q charge due to the other two charges.

e.

Charge +q is now moved along the positive x–axis to a very large distance from the other two charges. The 3 magnitude of the force on the +q charge at this large distance now varies as 1/x . Explain why this happens.

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2009B2. Two small objects, labeled 1 and 2 in the diagram above, are suspended in equilibrium from strings of length L. Each object has mass m and charge +Q. Assume that the strings have negligible mass and are insulating and electrically neutral. Express all algebraic answers in terms of m, L, Q, q , and fundamental constants. a.

On the following diagram, sketch lines to illustrate a 2–dimensional view of the net electric field due to the two objects in the region enclosed by the dashed lines.

b.

Derive an expression for the electric potential at point A, shown in the diagram at the top of the page, which is midway between the charged objects.

c.

On the following diagram of object 1, draw and label vectors to represent the forces on the object.

d. Using the conditions of equilibrium, write—but do not solve—two equations that could, together, be solved for q and the tension T in the left–hand string.

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2001E1. A thundercloud has the charge distribution illustrated above left. Treat this distribution as two point charges, a negative charge of –30 C at a height of 2 km above ground and a positive charge of +30 C at a height of 3 km. The presence of these charges induces charges on the ground. Assuming the ground is a conductor, it can be shown that the induced charges can be treated as a charge of +30 C at a depth of 2 km below ground and a charge of –30 C at a depth of 3 km, as shown above right. Consider point P 1, which is just above the ground directly below the thundercloud, and point P 2, which is 1 km horizontally away from P1. a. b.

Determine the direction and magnitude of the electric field at point P 1. i. On the diagram, clearly indicate the direction of the electric field at point P 2 ii. How does the magnitude of the field at this point compare with the magnitude at point P 1? Justify your answer: ____ Greater

____Equal

____ Less

c. Letting the zero of potential be at infinity, determine the potential at these points. i. Point P1 ii. Point P2 d. Determine the electric potential at an altitude of 1 km directly above point P1. e. Determine the total electric potential energy of this arrangement of charges.

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2

–2

2002B5B. Two parallel conducting plates, each of area 0.30 m , are separated by a distance of 2.0 × 10 m of air. One plate has charge +Q; the other has charge –Q. An electric field of 5000 N/C is directed to the left in the space between the plates, as shown in the diagram above.

a.

Indicate on the diagram which plate is positive (+) and which is negative (–).

b.

Determine the potential difference between the plates.

c.

Determine the capacitance of this arrangement of plates.

An electron is initially located at a point midway between the plates.

d.

Determine the magnitude of the electrostatic force on the electron at this location and state its direction.

e.

If the electron is released from rest at this location midway between the plates, determine its speed just before striking one of the plates. Assume that gravitational effects are negligible.

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