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The Canterbury Episcopal School
Scope and Sequence
AP Physics II
Text: Physics, Principles with Applications, Giancoli, Douglas C., 6th Edition, Pearson/PrenticeHall, 2005.
AP Physics II begins seamlessly where Honors Physics I left off the previous school year.
Specifically, students are reminded, as a review, of:
● notation of concepts in mechanics and heat
● the table of analogies between the equations of linear motion and the equations of rotary motion
● the use of their Honors Physics I notes as a major resource for AP Physics II
Students are presented velocity as v = dx/dt and acceleration as a = dv/dt = d2s/dt2. Then,
applying linear and rotary motion from the table of analogies, students are able to solve problems
using the calculus-based equations for:
● the equations x(t), v(t), a(t), KE(t), and PE(t) for mass-on-spring SHM from a model of circular motion
featuring the variable θ = ωt
● the equations θ(t), v(t), a(t), KE(t), and PE(t) for simple pendulum SHM from a model of circular motion
featuring the variable φ = ωt
Students are reminded of wave properties, but now the mechanical nature of waves is
emphasized using the properties of SHM. Students work problems finding:
● the intensity I, the energy E, and the power P of a wave propagating through a medium of density ρ
● the relationships among I, E, and P for such a wave
● the speed of a wave along a rope-like medium in terms of the rope’s linear density (µ) and the force of
tension, FT, on the rope
● frequencies of harmonics and overtones of standing waves in a rope-like medium
● a comparison of predicted standing wave properties to measured properties of a vibrating string in the lab
Students are reminded of the wave behaviors of reflection and refraction as a basis for the
derivation of the Mirror Equation and the Lens Equation, which are shown side-by-side to be the
same derivation. Hence, students understand one equation covers both mirrors and lenses, as
does the auxiliary magnification equation. Using these two equations students demonstrate the
ability to:
● apply the special focal length to plane mirrors and the special distance length to telescopes and
microscopes
● solve all mirror problems involving focal length f, distance length d o, and image length di for:
> concave mirrors of radius of curvature r
> convex mirrors of radius of curvature r
● solve all lens problems involving focal length f, distance length do, and image length di for:
> convex lenses of radius of curvature r
> concave lenses of radius of curvature r
● correctly and consistently apply the sign conventions to all mirror and lens problems
● successfully conduct a lab confirming mirror and lens configurations on a simple optical bench using
the mirror/lens and the magnification equations
Students solve problems describing:
● double-slit diffraction
● single-slit diffraction
● diffraction by gratings
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A new fundamental unit of charge (in coulombs, or C) is introduced and added to the previous
four (m, kg, sec, TK). Students understand:
● static electricity and electric current in terms of coulombs
● modes of charge transfer
> a current of charge (I)
> charge induction
> by contact
● the nature of charge, the nature of charge transfer, and the nature of both electrical fields and electrical
forces by taking measurements from a Van de Graaff generator
The “three-column” method of covering “three chapters in the book at once” is introduced as a
new way to take notes, a way to cover material more efficiently, and a way emphasizing
analogous concepts that are treated in separate sections of most textbooks rather than
simultaneously. Students are introduced to concepts and equations in sets of three:
● field sources mass (m), charge (q), and charge-velocity (qv) or current-length (Il)
● forces by fields, gravitation force F g (Newton’s Universal Law of Gravitation), electrical force FE
(Coulomb’s Law), and the magnetic force FB (Biot-Savart Law)
● force constants, G, k = 1/4πεo, and k’ = µo/4π (εo and µo defined)
● FB re-expressed as a cross product between velocity v and magnetic field B
● the fields themselves, |g| = g, |E| = E, & |B| = B (g = gravitational field, E = electric field)
● forces as (field source)(field), so Fg = mg, FE = qE, & FB = qvB sin θ or IlB sin θ
● variations of FB as a cross product:
> FB = q v x B
> FB = I l x B
> FB = l I x B
> direction of FB determined by the right-hand rule
● the measurement of FB on a beam of electrons in a simple cathode ray tube immersed in a magnetic
field
Students are able to calculate forces due to fields:
● solve problems finding and involving F g
● solve problems finding and involving FE
● solve problems finding and involving FB
> FB in magnitude form or sin θ form
> FB in cross product or i, j, k form
* utilizing special 3 x 3 determinate to calculate cross product
* expanding about the 1st row always involving i, j, and k
Students calculate the fields themselves:
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find g’s from the Universal Law of Gravitation
find E’s from Coulomb’s Law
find B’s around current-carrying wires
using B’s to find forces, currents, and B’s between, within and around current-carrying wire conductors
use sophisticated mathematical techniques as shortcuts to finding fields
> calculate field fluxes with the general form of Gauss’s Law (a dot product)
> calculate g’s inside, on, and outside planets using Gauss’s Law for gravitational fields
> calculate E’s inside, on, and outside various charged conductors using Gauss’s Law for electric fields
> understand that the “loop nature” of B’s means Gauss’s Law for B is zero
> calculate B’s in continuous loops around current I and within current densities J using Ampere’s Law
> calculate B inside a solenoid using Ampere’s Law
● create a magnetic field around a conductor carrying a high amp load, verifying it with iron filings and a
galvanometer
● measure the magnetic field B inside a solenoid of a modest number of wire turns with a galvanometer
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Using the analogies of potential ( [energy/ field source] = [field][distance] ) and potential energy
( [field source][potential] = [force][distance] = [field source][field][distance] ), students in the
process of solving problems are able to calculate:
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gravitational potential energy Ug ( = mgh) and gravitational potential U g/m
the field g as the spatial derivative of gravitational potential Ug/m
the gravitational force Fg as the spatial derivative of gravitational potential energy Ug
electric potential or voltage, V, and electric potential difference ΔV in unit of volts, V (V = J/C)
electric potential energy as qΔV or qV
the field E as the spatial derivative of electrical potential V
the electrical force FE as the spatial derivative of electric potential energy qV
values in problems utilizing the units expression linking mechanical dynamics with electrodynamics
(J = Nm = CV)
The concept of electrical capacitance C = Q/V (units of farads = F = C/V) is introduced, and
students demonstrate their ability to solve problems:
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using a new unit of energy, the electron volt (eV), appropriate for the atomic scale
finding the capacitance and the voltage between charged parallel conductor plates
using different values of dielectric constants κ and the definition of ε as compared to ε o
calculating the energy and energy/volume stored in a capacitor
The motion of the path of a mass m with charge q moving at speed v perpendicular to the
direction of a magnetic field B and simultaneously perpendicular to an electric field E is
described, as well as the same mass moving perpendicular only to a magnetic field B are
described for the student. By the resulting formulas the students can calculate:
● the speed v in terms of the two fields B & E
● the “drift velocity” in B & E due to the Hall Effect
● the cyclotron frequency f and period T, as well as m, r, q, v, or B of the mass moving only perpendicular
to a B in a circular path
● the Hall Effect using a Hall effect apparatus
The concept of [torque] = [dipole (moment)][field] = [field source][distance][field] =
[distance][force], whose direction is determined by the right-hand rule, is used to derive the
torques (cause of rotary motion) for the three fields, so that students can solve problems finding:
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gravitational torque or τg = mrg sin θ = |τg| = |r x Fg| = |r x mg| = |mr x g| ( = Iα)
gravitational potential Ug/m in terms of gravitational dipole
electric field torque or τE = QlE sin θ = pE sin θ = |τE| = |l x FE| = |l x QE| = |p x E| ( p = |p| = Ql = |Ql|)
electric potential V in terms of electric dipole
magnetic torque on N conducting rectangular loops of dimensions l & w area A = lw, which is
τB = NIAB sin θ = |τB| = |NI A x B| = |NQv/l A x B| = |NQA/l v x B| = |NQw v x B| = Nw|Q v x B|
= Nw|FB|
Through magnetic dipoles and the magnetic analogy of ε, µ, permanent magnetism in ferro- and
non-ferro-magnetic materials is understood by students as the result of orbital electrons in all
magnetic materials. Students demonstrate their understanding of:
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the effects of magnetic materials inside a solenoid
the differences among ferromagnetic, paramagnetic, and diamagnetic materials in terms of µ
hysteresis
the geometry of magnetic fields and their N and S poles, using permanent magnets and iron filings
Electrical circuits are defined and the rules of circuitry given, so that students are able to solve
problems:
● finding equivalent capacitances for capacitors wired both in series and parallel
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● finding equivalent capacitances for capacitors wired in combinations of series and parallel sections
● finding the resistance R (units of Ohms = Ω) of wires of various densities, lengths, and cross sectional
area
● using Ohm’s Law (V = IR)
● using all three forms of power equations for circuits (P = IV = I2R = V2/R)
● expressing AC (alternating current) values of V and I as V(t) and I(t) expressed as trig functions
● finding equivalent resistances for resistors wired both in series and parallel
● find equivalent resistances for resistors wired in combinations of series and parallel sections
● applying Ohm’s Law to solve for currents in each branch of simple DC (direct current) circuits
● calculating electromotive forces (emf’s), internal resistances, and terminal voltages for voltage sources
in DC circuits (for batteries)
● solving general (more complicated) DC circuits using Kirchoff’s Laws of Circuitry with Ohm’s Law
> Kirchoff’s First Law (junction rule)
> Kirchoff’s Second Law (loop rule)
● solving actual DC circuits connected in the lab using various resistors, ammeters, voltmeters, and
voltage sources
● reading the value of resistance from the code of stripes printed upon the resistors ( using the mnemonic
BBROYGBVGW)
Michael Faraday’s discovery of induction (induced emf = E) is presented for the students, so that
they can solve problems that:
● calculate magnetic flux ΦB = BA cos θ = B ● A
● utilize Faraday’s Law of Induction, given by E = - N ΔΦB/Δt = -N dΦB/dt (N = # of coils or loops)
> when B varies with time
> when the area of flux is altered in time
> when the conductor is moved in time
● involve electric guitar “pick-ups”
● utilize Lenz’s Law, which determines the direction of the induced current
● calculate E for a conductor moving in simple geometry, using the principle of the electric motor
● calculate E for an AC generator using magnetic torque τB
● utilize the transformer equation, which is derived from Faraday’s Law
>step-up transformers
>step-down transformers
● verify the transformer equation using measurements made in the lab
● verify Faraday’s Law by moving conductors in the lab through a magnetic field and by using an AC
source to generate the magnetic field B
Mutual inductance (M) and self inductance (L) (in units of Henrys = H) are introduced to the
students using Faraday’s Law and Lenz’s Law. A new member of circuitry, the inductor, L, is
written in terms of the voltage, V or E, across it, E = - LΔI/Δt = - LdI/dt. Using this equation,
circuit problems are expanded so that the student can:
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calculate L for solenoids
find the energy stored in a magnetic field B
find the energy stored in a solenoid
calculate the magnetic energy density (in J/m3) for a solenoid and in general
The expression for the charge Q(t) discharging through a resistor R in a closed RC circuit is
derived for the students as a solution of a simple differential equation, and this Q(t) is used as the
basis for students being able to:
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derive for themselves the equations I(t) using a derivative and the equation V(t) using Ohm’s Law
calculate the mean life (capacitive time constant) and half life of the discharge (and build-up)
recognize that at t = 0 it is as if C is not there and at large t as if R is not there
calculate Q, I, and V for the circuit for any time t
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● find the equations V(t), Q(t), and I(t) for a charging capacitor wired in series with an R and a voltage
● calculate Q, I, and V for the charging capacitor circuit for any time t
● verify the formula for the capacitive time constant in the lab with a RC circuit and a timer
A RL circuit with a voltage and a closed RL circuit with current I(t) decaying through the R is
analyzed for the students in a parallel way the RC circuit was analyzed. This analysis is the basis
for the students demonstrating their ability to:
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calculate any value of I(t) at any time t
calculate the mean life (inductive time constant) and half life of the build-up (and discharge)
recognize that at t = 0 it is as if the R is not there and at large t as if L is not there
use calculus and Ohm’s Law to derive the voltage across the inductor V L(t) and the voltage across the
resistor VR(t)
● use calculus to derive the decaying current I(t) in the closed RL circuit
● calculate I and V at any time t for both the built-up and discharge RL circuits
● verify the formula for the inductive time constant in the lab with a RL circuit and a timer
Students demonstrate the ability to understand the concept of LC circuitry resonance as
analogous to SHM and to calculate the values of:
● resonance frequency
● the charge Q(t) undergoing SHM in the circuit
Students demonstrate understanding of and calculation within a series RLC circuit driven by an
alternating emf. Students can calculate:
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capacitive reactance XC
inductive reactance XL
total impedance Z
the resonance frequency of the RLC circuit and apply it to the concept of tuning in the circuit
Students combine the fields E and B to form the structure of all electromagnetic radiation,
including visible light, TV signals, radio signals, X-rays, and gamma rays. Upon this basis
students can find values of:
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the speed of light in a vacuum and in a medium in terms of εo, ε, µo, and µ
the speed of light as the ratio E/B
energy density of electromagnetic radiation in terms of E or B
intensity of electromagnetic radiation in terms of E or B
the Poynting Vector S = (1/µo) E x B for electromagnetic radiation
Students are exposed to a brief introduction to Maxwell’s Equations. Students demonstrate that
they know:
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the four equations completely describe electromagnetic radiation
the equations are written as vector calculus operations on E and B
how to identify the operations of grad, gradient, divergence, and curl
how to recognize the differential form of Maxwell’s Equations
how to recognize the integral form of Maxwell’s Equations