AP Physics C E&M Standards

A. Electrostatics .....................................................................30%

1. Charge, field, and potential
2. Coulomb's law and field and potential of point charges
3. Fields and potentials of other charge distributions

a. Planar
b. Spherical symmetry *
c. Cylindrical symmetry *

4. Gauss's law *

AP Physics C E&M Standards

A. Electrostatics (continued).....................................................................30%

1. Charge, field, and potential
2. Coulomb's law and field and potential of point charges
3. Fields and potentials of other charge distributions

a. Planar
b. Spherical symmetry *
c. Cylindrical symmetry *

4. Gauss's law *

Electric Field

Essential Question: How is knowledge of electric fields useful?

State the general convention for the type of charge used in defining electrical phenomena. positive charge Define electric field and note how its equation is analogous to g = F / m in mechanics. Map of force on a + test charge E-field is a vector E ≡ F / q Draw the electric field lines ( E-field rays) around point charges. State the meaning of the arrows and the spacing between lines in an electric field diagram. arrows: are rays indicating the direction of force on a hypothetical positive charge spacing between lines: is proportional to e-field strength Use Coulomb's law to calculate the electric field around a point charge. Calculate the electric field: along the axis through the center of a thin concentric charged ring radius = a -- model: ring of point charges E = kQx / (a2 + x2)3/2 along the axis through the center of concentric charged disk of radius = R -- model: series of thin concentric rings E = 2πkσ [ 1 - x / (R2 + x2)1/2 ] infinitely large flat surface  -- model: disk with an infinite radius E = 2πkσ Geometry E-field Direction point charge E =    (kQ) / (r2) radially outward from charge infinite Line with uniform charge E =   (2kλ) / (r1) perpendicular to line infinite plane with uniform charge E = (2πkσ) / (r0) perpendicular to plane Formative Assessment: Group and individual problem solving on white boards. Homefun: prob 15, 19, 23, 41, 43 p.675-6 Serway Relevance: Electric fields are a basic principle in photocopiers, electrostatic precipitators, lighting rods, wireless communications, etc.

Video: Demonstration of Electrostatic Precipitators Electrostatic precipitators are used for removing smoke, pollen, bacteria, or other particles from air. they charge the particles which are then attracted to oppositely charged plates. Video--lab demo Video--application Question: Why would the electric field be particularly strong around a pointed electrode? Answer: The charge on a conductive sphere will distribute equally & can be modeled as a point charge at the center. Hence, at the surface E = (kQ)/(R^2). As R approaches 0 (in other words becomes pointed), E approaches ∞. Why are lightning rods generally pointed? Video--lightning rod

11. State the value of the e-field and force on a charged particle placed at any location above an infinitely large flat surface with a uniform charge.
12. Solve kinematics problems for a charged particle in a uniform e-field.
13. Solve projectile motion problems for a charged particle in a uniform e-field.
14. Solve mechanical energy problems for a charged particle in a uniform e-field.

Formative Assessment: Group and individual problem solving on white boards.

Homefun: prob 37, 45, 51, 53

Relevance: Charged particle kinematics are a basic principle in CRT based TVs, x-ray tubes, and a host of electronic instruments such as oscilloscopes, mass spectrometers, etc.

1) Describe 3 ways to characterize a "solid" object.

• Volume
• Surface area
• Cross Sectional area

2) Define scale up factor (SUF). When an object is scaled up every dimension is multiplied by the same factor. This factor is called the scale up factor. An object scaled up in this manner will look the same as it's smaller version.

3) Develop a general scale up relationships for the 3 characteristics of solid objects.

• Volume: Scales up by (SUF)^3
• Surface area: Scales up by (SUF)^2
• Cross Sectional area: Scales up by (SUF)^2

4) Describe the key variable in an animal's weight and tell why it is not density.

• Animals are mostly water, hence they have similar densities

5) State the key factor in a warm blooded animal's heat loss.

• Surface area

6) Describe the relationship between heat loss and food intake.

• Heat loss is a major factor in minimum food intake

7) Describe the key factors in respiration.

• The lungs have a fractal type design to maximize surface area

8) State how the compressive strength of leg bones scales up.

• Bone strength is directly proportional to cross sectional area and Scales up by (SUF)^2

9) State why animals can not be scaled up and down by large factors.

• Strength of legs
• Heat loss
• Food intake
• Respiration

10) Analyze an animal's form using a knowledge of scale up factors.

• Mass/weight
• Surface area
• Cross section of leg

Homefun: Work the Scale Up Factors Problems

Read: Insultingly Stupid Movie Physics

Chapter 4, Scaling: Big bugs and little people, pp 51 - 66

Relevance: Scale up is a major issue in virtually all design areas, pilot plant studies, or studies based on any type of scale model such as those used in wind tunnels.

AP Physics C E&M Standards

1. Define electric flux--roughly speaking, the amount of electric field passing through a given surface.

• Area is considered a vector whose direction is normal to the surface.
• Dot product between E-field and area vector
• Flux = E A cos(θ)   (This is a dot product, hence, flux is a scalar.)

2. State the relationship between electric flux through a closed surface and the enclosed charge.

Gauss's Law:	Electric flux through a closed Gaussian surface is directly proportional to the enclosed charge (Q).		Closed Gaussian surfaces are imaginary "bubbles" used for determining E-fields. The bubbles can be any shape including cubes, cylinders, or spheres as show above.
	∮E • da	= 4πkQ
		= Q /εo
	where:
	εo	= 1/(4πk)
		= permittivity of free space
		= 8.8542 x 10-19 C2/(N m2)

 

Homefun: Read 24.1 to 24.2

Questions 1-7 p.685; Problems 1, 3, 7 p. 686-687

 

E-Fields in and around: planes, non-conductive spheres, conductive spheres, and cylinders Solve for the electric flux created by a point charge through an infinitely large plane. ( E = 2πkQ ) Solve for the electric flux created by a point charge next to finite sized plane. ( E = 2πkQ ) Using Gauss's law derive the E-field around a point charge. ( E = kQ / r2 ) Derive an expression for the electric field inside and outside a charged "fuzzy" sphere. ("fuzzy" sphere = uniformly charged non-conductive sphere) State the electric field inside a conductor in electrostatic equilibrium. (Hints: where does the charge go in a conductive object? Will there be any charge inside a Gaussian surface placed just inside of the object's surface?) Derive an expression for the E-field inside and outside a charged hollow conductive sphere. (Hint: how much charge is enclosed inside the hollow sphere?) Derive an expressions for the E-field inside and outside both very long fuzzy cylinders and conductive cylinders. (outside: E = (2kλ) / (r1))   Formative Assessment: Group and individual problem solving on white boards. Homefun: Read 24.3 to 24.4 Problems 11, 13, 15, 27, 45 pp. 687-688 Relevance: Gauss's Law is a powerful tool for calculating e-field strengths. This is an important issue in shielding from random electronic noise, antennae design, and wireless communication.     Essential Question: How are gravity fields and electric fields similar?

E-Fields in and around: planes, non-conductive spheres, conductive spheres, and cylinders Be as one with the info in table 24.1 p. 697. Be as one with the four magic box points on pages 693, 694. Derive an expressions for the E-field inside and outside both fuzzy and conductive concentric spherical shells. Derive an expressions for the E-field inside and outside both fuzzy and conductive inner spheres with concentric cylindrical outer shells. The outer surface of the outer shell acts like a point charge to the outside world. All the charges inside the outer shell are completely hidden or shielded from the outside world.     Formative Assessment: Group and individual problem solving on white boards. Homefun: Problems 31, 39, 47 p. 688-689 Relevance: Note that the equation for e-field inside a non-conductive sphere with a uniform charge distribution (fuzzy sphere) is essentially identical to the derivation for the g-field inside a planet. We could create a Gauss's law of gravity.   Review of E-field Derivations Based on gauss's Law Summative Assessment: Unit exam objectives 1-13

Demo: Shielding Turn on a transistor radio and place it a  atop a clean paint can lid. Slowly lower a clean empty paint can over the radio until the can contacts the lid. Why does the radio lose its signal? How is does the radio and can  demo different from the Gauss's Law analysis of shielding?