2027 exam · Equation sheet

AP® Physics 2: Algebra-Based equation sheet (2027), explained

The official Physics 2 sheet has a page of constants, unit symbols, prefixes, common trig values and exam conventions, then pages for electricity, magnetism, thermal physics, waves and optics, modern physics, geometry, and mechanics and fluids. Below, every Physics 2 equation and constant is explained: what each letter means, its unit, when to use it, the classic mistake, and where we teach it. The mechanics and geometry parts are the same as on the Physics 1 sheet, so we link to that page instead of repeating them.

The official sheet: AP Physics 2: Algebra-Based Exam Reference Information (PDF, College Board) (opens in a new tab). Keep it open next to this page. We link to it instead of copying it, so you always see College Board's current version.

Checked against the 2027 version on October 5, 2026. The explanations are ours, not College Board's.

Using the sheet on exam day

You have the sheet for the whole exam, on paper and in the testing app. Learn the order before exam day: constants and conventions first, then electricity, magnetism and thermal physics, then waves, optics, modern physics and geometry, then mechanics and fluids.
Read the conventions box once. Unless a question says otherwise: ideal gases are monatomic (that's why $U = \frac{3}{2}nRT$ works), electric potential is zero infinitely far from a point charge, capacitors are air-filled with $\kappa = 1.0$ , resistors and bulbs are ohmic, current is conventional current, and the small-angle approximation is fine for single and double slits.
For photons with wavelengths in nm, use $hc = 1240\ \text{eV}\cdot\text{nm}$ from the constants table: a photon's energy in eV is 1240 divided by its wavelength in nm.
The sheet gives equations, not rules. It won't tell you which way a magnetic force points, which sign to give a focal length, or when an image is virtual. Those you have to know.
The first page also has a prefix table (pico to tera) and the sine, cosine and tangent of 0°, 30°, 37°, 45°, 53°, 60° and 90°. Use them for conversions like nm to m or μC to C, and to skip the calculator on easy angles.

Constants and conversions

Avogadro's number: $\displaystyle N_0 = 6.02\times 10^{23}\ \text{mol}^{-1}$; Use it to switch between a number of moles and a number of molecules or atoms, like going between the two forms of the ideal gas law.
Universal gas constant: $\displaystyle R = 8.31\ \text{J}/(\text{mol}\cdot\text{K})$; Use it in $PV = nRT$ and $U = \frac{3}{2}nRT$ when the amount of gas is given in moles.
Boltzmann's constant: $\displaystyle k_B = 1.38\times 10^{-23}\ \text{J/K}$; Use it when you're counting molecules instead of moles, and for the average kinetic energy of one molecule, $K_{\text{avg}} = \frac{3}{2}k_B T$ .
One atmosphere of pressure: $\displaystyle 1\ \text{atm} = 1.0\times 10^{5}\ \text{N/m}^2 = 1.0\times 10^{5}\ \text{Pa}$; Use it to convert pressures given in atmospheres into pascals before using the gas equations.
Coulomb constant: $\displaystyle k = \frac{1}{4\pi\varepsilon_0} = 9.0\times 10^{9}\ \frac{\text{N}\cdot\text{m}^2}{\text{C}^2}$; Use it in Coulomb's law and in the field, potential and potential energy of point charges. It's the same number as the 1/(4πε₀) out front.
Proton mass: $\displaystyle m_p = 1.67\times 10^{-27}\ \text{kg}$; Use it for a proton's momentum, kinetic energy or acceleration in a field, and in nuclear mass comparisons.
Neutron mass: $\displaystyle m_n = 1.67\times 10^{-27}\ \text{kg}$; Use it for neutrons in nuclear problems. To three figures it matches the proton mass.
Electron mass: $\displaystyle m_e = 9.11\times 10^{-31}\ \text{kg}$; Use it for an electron's speed, momentum or de Broglie wavelength, and in the Compton equation.
Elementary charge: $\displaystyle e = 1.60\times 10^{-19}\ \text{C}$; Use it as the size of the charge on one proton or one electron (the electron's is negative), and to count how many electrons make up a charge.
Vacuum permittivity: $\displaystyle \varepsilon_0 = 8.85\times 10^{-12}\ \text{C}^2/(\text{N}\cdot\text{m}^2)$; Use it in the parallel-plate capacitor equations, $C = \kappa\varepsilon_0\frac{A}{d}$ and $E_C = \frac{Q}{\kappa\varepsilon_0 A}$ .
Vacuum permeability: $\displaystyle \mu_0 = 4\pi\times 10^{-7}\ (\text{T}\cdot\text{m})/\text{A}$; Use it for the magnetic field around a long straight wire, $B = \frac{\mu_0 I}{2\pi r}$ . Keep the $4\pi$ in; it often cancels.
One electron volt: $\displaystyle 1\ \text{eV} = 1.60\times 10^{-19}\ \text{J}$; Use it to convert between electron volts and joules, which comes up in nearly every photon and photoelectric problem.
Planck's constant: $\displaystyle h = 6.63\times 10^{-34}\ \text{J}\cdot\text{s} = 4.14\times 10^{-15}\ \text{eV}\cdot\text{s}$; Use it in $E = hf$ , $\lambda = \frac{h}{p}$ and the photoelectric and Compton equations. Pick the J·s value for joules and the eV·s value for electron volts.
Planck's constant times the speed of light: $\displaystyle hc = 1.99\times 10^{-25}\ \text{J}\cdot\text{m} = 1240\ \text{eV}\cdot\text{nm}$; Use it for a photon's energy straight from its wavelength, $E = \frac{hc}{\lambda}$ . With λ in nm, the 1240 eV·nm value gives the energy in eV in one step.
Speed of light: $\displaystyle c = 3.00\times 10^{8}\ \text{m/s}$; Use it for light and all electromagnetic waves in vacuum, in the index of refraction $n = \frac{c}{v}$ , and in $E = mc^2$ .
Wien's constant: $\displaystyle b = 2.90\times 10^{-3}\ \text{m}\cdot\text{K}$; Use it in Wien's law, $\lambda_{\text{max}} = \frac{b}{T}$ , to link a hot object's temperature to the wavelength where it glows brightest.
Stefan-Boltzmann constant: $\displaystyle \sigma = 5.67\times 10^{-8}\ \text{W}/(\text{m}^2\cdot\text{K}^4)$; Use it in $P = A\sigma T^4$ for the power radiated by a blackbody.
One unified atomic mass unit: $\displaystyle 1\ \text{u} = 1.66\times 10^{-27}\ \text{kg} = 931\ \text{MeV}/c^2$; Use it to turn nuclear masses given in u into kilograms, or straight into energy: 1 u of missing mass releases 931 MeV.
Universal gravitational constant: $\displaystyle G = 6.67\times 10^{-11}\ \text{m}^3/(\text{kg}\cdot\text{s}^2) = 6.67\times 10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$; Use it in Newton's law of gravitation from the mechanics page, for example to compare gravity with the electric force between two particles.
Acceleration due to gravity at Earth's surface: $\displaystyle g = 9.8\ \text{m/s}^2$; Use it for the weight of a charged object or the free-fall part of a problem, like a charged drop held up by an electric field.
Gravitational field strength at Earth's surface: $\displaystyle g = 9.8\ \text{N/kg}$; It's the same number as the acceleration, written as force per kilogram. Use it to compare with an electric field, which is force per coulomb.

Electric force, field, and potential

Coulomb's law, electric fields, potential energy, potential and capacitors. The exam takes the potential to be zero infinitely far from an isolated point charge.

Electric force between two point charges

\displaystyle \lvert \vec{F}_E \rvert = \frac{1}{4\pi\varepsilon_0}\frac{\lvert q_1 q_2 \rvert}{r^2} = k\frac{\lvert q_1 q_2 \rvert}{r^2}

What the symbols mean

$\vec{F}_E$: electric force each charge exerts on the other; Unit: N
$q_1, q_2$: the two charges; Unit: C
$r$: distance between the centers of the charges; Unit: m
$\varepsilon_0$: vacuum permittivity; Unit: C²/(N·m²)
$k$: Coulomb constant; Unit: N·m²/C²

Use it when: Use it when two small charged objects are a known distance apart and you need the size of the force on each. Find the direction separately: like charges repel, unlike charges attract.

Watch out: Forgetting to square r, or leaving charges in μC. If r doubles, the force drops to a quarter, not a half; and 1 μC is 10⁻⁶ C.

Try it: Charges of +2.0 μC and −3.0 μC are 0.30 m apart. How big is the force between them?

Answer: $F = k\frac{\lvert q_1 q_2 \rvert}{r^2} = (9.0\times 10^{9})\frac{(2.0\times 10^{-6})(3.0\times 10^{-6})}{(0.30)^2} = 0.60\ \text{N}$ . The charges are opposite, so the force pulls them together.

Learn it: 10.1 Electric Charge and Electric Force

Electric field from force

\displaystyle \vec{E} = \frac{\vec{F}_E}{q}

What the symbols mean

$\vec{E}$: electric field at a point; Unit: N/C
$\vec{F}_E$: electric force on a charge placed at that point; Unit: N
$q$: the charge feeling the force; Unit: C

Use it when: Use it to go between field and force. If you know the field at a point, $\vec{F}_E = q\vec{E}$ gives the force on any charge you put there.

Watch out: Ignoring the sign of q. A negative charge feels a force opposite to the field direction.

Learn it: 10.3 Electric Fields

Electric field of a point charge

\displaystyle \lvert \vec{E} \rvert = \frac{1}{4\pi\varepsilon_0}\frac{\lvert q \rvert}{r^2} = k\frac{\lvert q \rvert}{r^2}

What the symbols mean

$\vec{E}$: electric field made by the charge; Unit: N/C
$q$: the charge making the field; Unit: C
$r$: distance from the charge to the point; Unit: m
$k$: Coulomb constant; Unit: N·m²/C²

Use it when: Use it for the field strength a distance r from one point charge. The field points away from a positive charge and toward a negative one.

Watch out: Adding the fields of several charges as plain numbers. Fields are vectors: draw each one's direction, then add components.

Learn it: 10.3 Electric Fields

Electric potential energy of two charges

\displaystyle U_E = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r} = k\frac{q_1 q_2}{r}

What the symbols mean

$U_E$: electric potential energy of the pair; Unit: J
$q_1, q_2$: the two charges, with their signs; Unit: C
$r$: distance between the charges; Unit: m

Use it when: Use it for the energy stored in a pair of charges, for example to find how fast a charge is moving after it's released, using energy conservation.

Watch out: Dropping the signs or squaring r. Unlike the force equation, this one keeps the signs (opposite charges give a negative $U_E$ ) and has r, not $r^2$ .

Learn it: 10.4 Electric Potential Energy · 10.7 Conservation of Electric Energy

Change in electric potential energy

\displaystyle \Delta U_E = q\Delta V

What the symbols mean

$\Delta U_E$: change in the charge's electric potential energy; Unit: J
$q$: charge that moves, with its sign; Unit: C
$\Delta V$: change in electric potential it moves through; Unit: V

Use it when: Use it when a charge moves through a potential difference, like an electron sped up through 100 V. Pair it with energy conservation: $\Delta K = -\Delta U_E$ .

Watch out: Sign slips with electrons. An electron (negative q) moving to higher potential loses potential energy, so it speeds up.

Learn it: 10.5 Electric Potential · 10.7 Conservation of Electric Energy

Electric potential from point charges

\displaystyle V = \frac{1}{4\pi\varepsilon_0}\sum_i \frac{q_i}{r_i}

What the symbols mean

$V$: electric potential at a point; Unit: V
$q_i$: each charge, with its sign; Unit: C
$r_i$: distance from that charge to the point; Unit: m

Use it when: Use it for the electric potential at a point near one or more point charges. Potential is a scalar, so add the terms with their signs.

Watch out: Squaring the distance or giving potential a direction. There's no $r^2$ and no direction here: just signed numbers added up.

Learn it: 10.5 Electric Potential

Electric field from potential difference

\displaystyle \lvert \vec{E} \rvert = \left\lvert \frac{\Delta V}{\Delta r} \right\rvert

What the symbols mean

$\vec{E}$: electric field; Unit: V/m (the same as N/C)
$\Delta V$: change in potential; Unit: V
$\Delta r$: distance moved along the field; Unit: m

Use it when: Use it when you know how the potential changes over a distance, like across two parallel plates, where the field is the voltage divided by the plate gap.

Watch out: Using a distance that isn't along the field. Measure Δr parallel to the field, and remember the field points toward lower potential.

Learn it: 10.5 Electric Potential

Capacitance

\displaystyle C = \frac{Q}{\Delta V}

What the symbols mean

$C$: capacitance; Unit: F
$Q$: size of the charge on either plate; Unit: C
$\Delta V$: potential difference between the plates; Unit: V

Use it when: Use it to link the charge on a capacitor to the voltage across it.

Watch out: Thinking C changes when Q or ΔV changes. Capacitance depends only on the capacitor's shape and what's between the plates; doubling ΔV doubles Q.

Learn it: 10.6 Capacitors

Capacitance of parallel plates

\displaystyle C = \kappa\varepsilon_0\frac{A}{d}

What the symbols mean

$C$: capacitance; Unit: F
$\kappa$: dielectric constant of the material between the plates; Unit: none
$\varepsilon_0$: vacuum permittivity; Unit: C²/(N·m²)
$A$: area of one plate; Unit: m²
$d$: distance between the plates; Unit: m

Use it when: Use it to find a parallel-plate capacitor's capacitance from its size, or to predict what happens when you move the plates or add an insulator. Unless told otherwise, the exam's capacitors are air-filled, so $\kappa = 1.0$ .

Watch out: Getting the direction backward: pulling the plates farther apart makes C smaller. Also convert cm² to m² by dividing by 10,000, not 100.

Learn it: 10.6 Capacitors

Electric field inside a parallel-plate capacitor

\displaystyle E_C = \frac{Q}{\kappa\varepsilon_0 A}

What the symbols mean

$E_C$: electric field between the plates; Unit: N/C
$Q$: size of the charge on either plate; Unit: C
$\kappa$: dielectric constant; Unit: none
$\varepsilon_0$: vacuum permittivity; Unit: C²/(N·m²)
$A$: area of one plate; Unit: m²

Use it when: Use it for the field between the plates when you know the charge on them. Away from the edges, the field is uniform.

Watch out: Expecting the field to change with the plate gap when the charge stays the same. With fixed Q, moving the plates apart doesn't change E; it raises ΔV instead.

Learn it: 10.6 Capacitors

Energy stored in a capacitor

\displaystyle U_C = \frac{1}{2}Q\Delta V

What the symbols mean

$U_C$: energy stored in the capacitor; Unit: J
$Q$: charge on either plate; Unit: C
$\Delta V$: potential difference across it; Unit: V

Use it when: Use it for the energy stored in a charged capacitor. Swap in $Q = C\Delta V$ to get $\frac{1}{2}C(\Delta V)^2$ when you know C instead of Q.

Watch out: Leaving off the ½. It's there because the charge went on while the voltage was still building up from zero.

Learn it: 10.6 Capacitors

Circuits

Current, resistance, power, combining resistors and capacitors, and RC circuits. The exam treats batteries, wires and meters as ideal and resistors and bulbs as ohmic.

Electric current

\displaystyle I = \frac{\Delta q}{\Delta t}

What the symbols mean

$I$: current; Unit: A
$\Delta q$: charge passing a point; Unit: C
$\Delta t$: time it takes; Unit: s

Use it when: Use it to turn an amount of charge passing a point in some time into a current, or the other way around.

Watch out: Pointing current the way electrons move. On this exam current is conventional current: it points the way positive charge would move, opposite to the electrons.

Learn it: 11.1 Electric Current

Resistance of a wire

\displaystyle R = \frac{\rho\ell}{A}

What the symbols mean

$R$: resistance; Unit: Ω
$\rho$: resistivity of the material; Unit: Ω·m
$\ell$: length of the wire; Unit: m
$A$: cross-sectional area of the wire; Unit: m²

Use it when: Use it when a problem changes a wire's length, thickness or material and asks how its resistance changes.

Watch out: Using the diameter as the radius in $A = \pi r^2$ . Halve the diameter first. Doubling the diameter makes A four times bigger, so R drops to a quarter.

Learn it: 11.3 Resistance, Resistivity, and Ohm’s Law

Electric power

\displaystyle P = I\Delta V

What the symbols mean

$P$: rate energy is used or supplied; Unit: W
$I$: current through the element; Unit: A
$\Delta V$: potential difference across the element; Unit: V

Use it when: Use it for how fast a resistor, bulb or battery transfers energy. With Ohm's law it becomes $P = I^2R$ or $P = \frac{(\Delta V)^2}{R}$ .

Watch out: Using the battery's voltage for one resistor's power. Use the current through and voltage across that one element. The brightest bulb is the one with the most power.

Learn it: 11.4 Electric Power

Current through a resistor

\displaystyle I = \frac{\Delta V}{R}

What the symbols mean

$I$: current through the resistor; Unit: A
$\Delta V$: potential difference across the resistor; Unit: V
$R$: resistance; Unit: Ω

Use it when: Use it for any ohmic resistor or bulb: know two of current, voltage and resistance, and find the third.

Watch out: Mixing quantities from different parts of the circuit, like the total voltage with one resistor's resistance. Keep all three about the same element, or all about the whole equivalent circuit.

Learn it: 11.3 Resistance, Resistivity, and Ohm’s Law

Resistors in series

\displaystyle R_{\text{eq},s} = \sum_i R_i

What the symbols mean

$R_{\text{eq},s}$: equivalent resistance of the series group; Unit: Ω
$R_i$: each resistance; Unit: Ω

Use it when: Use it for resistors in series, one after another on a single path, so the same current goes through each.

Watch out: Calling resistors series because they look lined up on the page. Series means no junction between them: all the current through one must go through the next.

Learn it: 11.5 Compound Direct Current (DC) Circuits

Resistors in parallel

\displaystyle \frac{1}{R_{\text{eq},p}} = \sum_i \frac{1}{R_i}

What the symbols mean

$R_{\text{eq},p}$: equivalent resistance of the parallel group; Unit: Ω
$R_i$: each resistance; Unit: Ω

Use it when: Use it for resistors in parallel, connected across the same two points so each has the same voltage across it.

Watch out: Forgetting to flip at the end. The sum gives one over the equivalent resistance, so take the reciprocal. The answer is always smaller than the smallest resistor.

Try it: A 6.0 Ω and a 3.0 Ω resistor are in parallel across a 12 V battery. What current does the battery supply?

Answer: $\frac{1}{R_{\text{eq},p}} = \frac{1}{6.0} + \frac{1}{3.0} = \frac{1}{2.0}$ , so $R_{\text{eq},p} = 2.0\ \Omega$ . Then $I = \frac{\Delta V}{R} = \frac{12}{2.0} = 6.0\ \text{A}$ .

Learn it: 11.5 Compound Direct Current (DC) Circuits

Capacitors in series

\displaystyle \frac{1}{C_{\text{eq},s}} = \sum_i \frac{1}{C_i}

What the symbols mean

$C_{\text{eq},s}$: equivalent capacitance of the series group; Unit: F
$C_i$: each capacitance; Unit: F

Use it when: Use it for capacitors in series. Each one holds the same charge, and the group acts like one capacitor with a wider plate gap, so the total is smaller.

Watch out: Using the resistor rules for capacitors. They're swapped: capacitors add as reciprocals in series and add directly in parallel.

Learn it: 11.8 Resistor-Capacitor (RC) Circuits

Capacitors in parallel

\displaystyle C_{\text{eq},p} = \sum_i C_i

What the symbols mean

$C_{\text{eq},p}$: equivalent capacitance of the parallel group; Unit: F
$C_i$: each capacitance; Unit: F

Use it when: Use it for capacitors in parallel, which act like one capacitor with a bigger plate area.

Watch out: Splitting the charge evenly. Parallel capacitors share the same ΔV, so the biggest capacitor holds the most charge.

Learn it: 11.8 Resistor-Capacitor (RC) Circuits

Time constant of an RC circuit

\displaystyle \tau = R_{\text{eq}}C_{\text{eq}}

What the symbols mean

$\tau$: time constant; Unit: s
$R_{\text{eq}}$: equivalent resistance the capacitor charges or discharges through; Unit: Ω
$C_{\text{eq}}$: equivalent capacitance; Unit: F

Use it when: Use it to say how quickly a capacitor charges or discharges through resistors. A bigger time constant means a slower change.

Watch out: Using a resistor that isn't in the charging path. Use the equivalent resistance of the path the capacitor's current actually takes.

Learn it: 11.8 Resistor-Capacitor (RC) Circuits

Magnetism

Magnetic forces on moving charges and wires, the field around a wire, magnetic flux and induced emf.

Magnetic force on a moving charge

\displaystyle F_B = qvB\sin\theta

What the symbols mean

$F_B$: magnetic force on the charge; Unit: N
$q$: the charge; Unit: C
$v$: speed of the charge; Unit: m/s
$B$: magnetic field; Unit: T
$\theta$: angle between the velocity and the field; Unit: degrees

Use it when: Use it for the force on a charge moving through a magnetic field. The force is perpendicular to both the velocity and the field; get its direction from the right-hand rule.

Watch out: Forgetting that a charge moving along the field feels no force, since $\sin 0^\circ = 0$ . And flip the right-hand-rule direction for a negative charge.

Learn it: 12.2 Magnetism and Moving Charges

Magnetic field around a long straight wire

\displaystyle B = \frac{\mu_0 I}{2\pi r}

What the symbols mean

$B$: magnetic field strength; Unit: T
$\mu_0$: vacuum permeability; Unit: T·m/A
$I$: current in the wire; Unit: A
$r$: distance from the wire; Unit: m

Use it when: Use it for the field strength a distance r from a long straight wire. The field circles the wire: point your right thumb along the current and your fingers curl the way the field goes.

Watch out: Using $r^2$ as in Coulomb's law. A long wire's field falls off as 1/r: double the distance, half the field.

Try it: A long straight wire carries 5.0 A. How strong is its magnetic field 0.10 m away?

Answer: $B = \frac{\mu_0 I}{2\pi r} = \frac{(4\pi\times 10^{-7})(5.0)}{2\pi(0.10)} = 1.0\times 10^{-5}\ \text{T}$ .

Learn it: 12.3 Magnetism and Current-Carrying Wires

Magnetic force on a current-carrying wire

\displaystyle F_B = I\ell B\sin\theta

What the symbols mean

$F_B$: magnetic force on the wire; Unit: N
$I$: current in the wire; Unit: A
$\ell$: length of wire inside the field; Unit: m
$B$: magnetic field; Unit: T
$\theta$: angle between the current and the field; Unit: degrees

Use it when: Use it for the force on a wire carrying current through a magnetic field, including two parallel wires pushing or pulling on each other.

Watch out: Using the whole wire's length when only part of it is in the field. ℓ is just the length inside the field.

Learn it: 12.3 Magnetism and Current-Carrying Wires

Magnetic flux

\displaystyle \Phi_B = \vec{B}\cdot\vec{A}

What the symbols mean

$\Phi_B$: magnetic flux through the loop; Unit: T·m²
$\vec{B}$: magnetic field; Unit: T
$\vec{A}$: area vector: as big as the loop's area, pointing straight out of its face; Unit: m²

Use it when: Use it to measure how much magnetic field passes through a loop. Flux is the starting point for every induction problem.

Watch out: Thinking the area vector lies along the loop. It's perpendicular to the loop's face, so a field straight through the face gives the most flux.

Learn it: 12.4 Electromagnetic Induction and Faraday’s Law

Magnetic flux with an angle

\displaystyle \Phi_B = \lvert \vec{B} \rvert \cos\theta \lvert \vec{A} \rvert

What the symbols mean

$\Phi_B$: magnetic flux through the loop; Unit: T·m²
$\vec{B}$: magnetic field; Unit: T
$\theta$: angle between the field and the area vector; Unit: degrees
$\vec{A}$: area vector of the loop; Unit: m²

Use it when: Use it to compute the flux when the field is tilted relative to the loop, or when a loop rotates in a field.

Watch out: Measuring θ from the plane of the loop instead of from the line perpendicular to it. If the field lies flat along the loop's surface, θ is 90° and the flux is zero.

Learn it: 12.4 Electromagnetic Induction and Faraday’s Law

Induced emf from changing flux

\displaystyle \lvert \varepsilon \rvert = \left\lvert \frac{\Delta\Phi_B}{\Delta t} \right\rvert

What the symbols mean

$\varepsilon$: induced emf; Unit: V
$\Delta\Phi_B$: change in magnetic flux through the loop; Unit: T·m²
$\Delta t$: time the change takes; Unit: s

Use it when: Use it when the flux through a loop changes, because B, the area or the angle changes, and you need the induced emf. Then $I = \frac{\varepsilon}{R}$ gives the induced current.

Watch out: Thinking a strong but steady field induces an emf. Only a changing flux does. The direction of the current comes from Lenz's law, which isn't on the sheet.

Learn it: 12.4 Electromagnetic Induction and Faraday’s Law

Emf of a rod moving through a field

\displaystyle \varepsilon = B\ell v

What the symbols mean

$\varepsilon$: induced emf across the rod; Unit: V
$B$: magnetic field; Unit: T
$\ell$: length of the rod; Unit: m
$v$: speed of the rod; Unit: m/s

Use it when: Use it for a conducting rod sliding through a magnetic field, with the rod, its velocity and the field all at right angles to each other.

Watch out: Using it when the motion isn't perpendicular to the field. If the rod moves along the field lines, it cuts no field and the emf is zero.

Learn it: 12.4 Electromagnetic Induction and Faraday’s Law

Thermal physics

Pressure, the ideal gas, heat flow and the first law of thermodynamics. Unless a question says otherwise, the exam's ideal gases are monatomic.

Pressure

\displaystyle P = \frac{F_\perp}{A}

What the symbols mean

$P$: pressure; Unit: Pa
$F_\perp$: force perpendicular to the surface; Unit: N
$A$: area the force acts on; Unit: m²

Use it when: Use it to connect the force a gas exerts on a wall or piston to its pressure. In kinetic theory, that force comes from molecules hitting the walls.

Watch out: Using a force that isn't perpendicular to the surface. Only the perpendicular part counts toward pressure.

Learn it: 9.1 Kinetic Theory of Temperature and Pressure

Average kinetic energy of a gas molecule

\displaystyle K_{\text{avg}} = \frac{3}{2}k_B T = \frac{1}{2}mv_{\text{rms}}^2

What the symbols mean

$K_{\text{avg}}$: average kinetic energy of one molecule; Unit: J
$k_B$: Boltzmann's constant; Unit: J/K
$T$: absolute temperature; Unit: K
$m$: mass of one molecule; Unit: kg
$v_{\text{rms}}$: root-mean-square speed of the molecules; Unit: m/s

Use it when: Use it to link a gas's temperature to how fast its molecules move. Two gases at the same temperature have the same average kinetic energy, so the lighter molecules move faster.

Watch out: Using °C. T must be in kelvin, so add 273. And m is one molecule's mass, not the whole sample's.

Learn it: 9.1 Kinetic Theory of Temperature and Pressure

Rate of heat flow by conduction

\displaystyle \frac{Q}{\Delta t} = \frac{kA\Delta T}{L}

What the symbols mean

$Q$: energy transferred by heating; Unit: J
$\Delta t$: time; Unit: s
$k$: thermal conductivity of the material; Unit: W/(m·K)
$A$: cross-sectional area heat flows through; Unit: m²
$\Delta T$: temperature difference between the two sides; Unit: K
$L$: thickness or length the heat travels through; Unit: m

Use it when: Use it for the rate energy flows through a slab or rod by conduction, like heat leaking through a window or wall.

Watch out: Mixing up this k with the Coulomb or Boltzmann constant. Here k is the material's thermal conductivity. Also, a thicker wall (bigger L) means slower heat flow, not faster.

Learn it: 9.3 Thermal Energy Transfer and Equilibrium · 9.5 Specific Heat and Thermal Conductivity

Ideal gas law

\displaystyle PV = nRT = Nk_B T

What the symbols mean

$P$: pressure; Unit: Pa
$V$: volume; Unit: m³
$n$: number of moles; Unit: mol
$R$: universal gas constant; Unit: J/(mol·K)
$T$: absolute temperature; Unit: K
$N$: number of molecules; Unit: none
$k_B$: Boltzmann's constant; Unit: J/K

Use it when: Use it to relate the pressure, volume and temperature of an ideal gas. Use the $nRT$ form with moles and the $Nk_B T$ form with a count of molecules.

Watch out: Plugging in liters, atmospheres or °C. Convert to m³ (1 L = 0.001 m³), Pa and K first.

Learn it: 9.2 The Ideal Gas Law

Internal energy of an ideal gas

\displaystyle U = \frac{3}{2}nRT = \frac{3}{2}Nk_B T

What the symbols mean

$U$: internal energy of the whole gas; Unit: J
$n$: number of moles; Unit: mol
$N$: number of molecules; Unit: none
$T$: absolute temperature; Unit: K

Use it when: Use it for the internal energy of an ideal monatomic gas, which is what the exam assumes. It shows that a gas's internal energy depends only on its temperature.

Watch out: Thinking U changes in a constant-temperature process. If T stays the same, ΔU = 0, so any heat in must leave as work.

Learn it: 9.4 The First Law of Thermodynamics

Work done on a gas

\displaystyle W = -P\Delta V

What the symbols mean

$W$: work done on the gas; Unit: J
$P$: pressure, held constant; Unit: Pa
$\Delta V$: change in the gas's volume; Unit: m³

Use it when: Use it for the work done on a gas at constant pressure. For any process, the size of the work is the area under the curve on a pressure-volume graph.

Watch out: Getting the sign backward. W is work done on the gas, so when the gas expands (ΔV positive), W is negative.

Learn it: 9.4 The First Law of Thermodynamics

First law of thermodynamics

\displaystyle \Delta U = Q + W

What the symbols mean

$\Delta U$: change in the system's internal energy; Unit: J
$Q$: energy transferred to the system by heating; Unit: J
$W$: work done on the system; Unit: J

Use it when: Use it for the energy bookkeeping in any gas process: energy in by heating, plus work done on the gas, equals the change in internal energy.

Watch out: Using the other textbook version, ΔU = Q − W, where W is work done by the gas. On this sheet W is work done on the gas, so it's a plus.

Try it: A gas absorbs 500 J by heating while it expands, doing 200 J of work on its surroundings. What is its change in internal energy?

Answer: The work done on the gas is $W = -200\ \text{J}$ , so $\Delta U = Q + W = 500 + (-200) = 300\ \text{J}$ .

Learn it: 9.4 The First Law of Thermodynamics

Heating with specific heat

\displaystyle Q = mc\Delta T

What the symbols mean

$Q$: energy transferred by heating; Unit: J
$m$: mass; Unit: kg
$c$: specific heat of the material; Unit: J/(kg·K)
$\Delta T$: change in temperature; Unit: K

Use it when: Use it when an object warms up or cools down without melting or boiling, and you need the energy, the mass or the temperature change.

Watch out: Using grams with a specific heat in J/(kg·K). Convert mass to kg. A change in temperature is the same size in °C and K, so ΔT needs no conversion.

Learn it: 9.5 Specific Heat and Thermal Conductivity

Waves and sound

Wave speed, period, how a wave looks in time and in space, waves on strings, and beats.

Wavelength, speed and frequency

\displaystyle \lambda = \frac{v}{f}

What the symbols mean

$\lambda$: wavelength; Unit: m
$v$: wave speed; Unit: m/s
$f$: frequency; Unit: Hz

Use it when: Use it to connect the wavelength, frequency and speed of any wave: sound, waves on a string, or light in a material.

Watch out: Thinking the frequency changes when a wave enters a new medium. The source sets the frequency; the speed and wavelength are what change.

Learn it: 14.2 Periodic Waves

Period and frequency

\displaystyle T = \frac{1}{f}

What the symbols mean

$T$: period, the time for one full cycle; Unit: s
$f$: frequency, cycles per second; Unit: Hz

Use it when: Use it to switch between period and frequency.

Watch out: Mixing this T up with temperature, which uses the same letter on the sheet. In wave problems, T alone is the period; tension is written with a subscript, as $F_T$ .

Learn it: 14.2 Periodic Waves

Displacement of an oscillating point over time

\displaystyle x(t) = A\cos(\omega t) = A\cos(2\pi ft)

What the symbols mean

$x$: displacement from the middle position; Unit: m
$A$: amplitude, the biggest displacement; Unit: m
$\omega$: angular frequency; Unit: rad/s
$t$: time; Unit: s
$f$: frequency; Unit: Hz

Use it when: Use it to describe how one point on a wave, or any oscillator, moves back and forth over time when it starts at its maximum displacement.

Watch out: Leaving the calculator in degree mode. The angle inside the cosine is in radians.

Learn it: 14.2 Periodic Waves

Shape of a wave in space

\displaystyle y(x) = A\cos\left(2\pi\frac{x}{\lambda}\right)

What the symbols mean

$y$: displacement of the medium at position x; Unit: m
$A$: amplitude; Unit: m
$x$: position along the wave; Unit: m
$\lambda$: wavelength; Unit: m

Use it when: Use it to describe a wave's shape at one instant: how far the medium is displaced at each position along it.

Watch out: Mixing up the two lengths: x is how far along the wave you are, and y is how far that point is displaced. And keep the calculator in radians.

Learn it: 14.2 Periodic Waves

Wave speed on a string

\displaystyle v_{\text{string}} = \sqrt{\frac{F_T}{m/\ell}}

What the symbols mean

$v_{\text{string}}$: speed of waves on the string; Unit: m/s
$F_T$: tension in the string; Unit: N
$m$: mass of the string; Unit: kg
$\ell$: length of the string; Unit: m

Use it when: Use it for the speed of a wave on a stretched string. Tighter strings carry faster waves; heavier strings carry slower ones.

Watch out: Forgetting the square root: four times the tension only doubles the speed. Also divide the string's mass by its length before using it.

Try it: A string under 100 N of tension has a mass per length of 0.010 kg/m. What is the wave speed, and what frequency gives a wavelength of 0.50 m?

Answer: $v = \sqrt{\frac{100}{0.010}} = 100\ \text{m/s}$ . Then $f = \frac{v}{\lambda} = \frac{100}{0.50} = 200\ \text{Hz}$ .

Learn it: 14.1 Properties of Wave Pulses and Waves · 14.6 Wave Interference and Standing Waves

Beat frequency

\displaystyle \lvert f_{\text{beat}} \rvert = \lvert f_1 - f_2 \rvert

What the symbols mean

$f_{\text{beat}}$: how many times per second the loudness rises and falls; Unit: Hz
$f_1, f_2$: frequencies of the two sounds; Unit: Hz

Use it when: Use it when two sounds with close frequencies play together and the loudness wobbles. The wobble rate is the difference of the two frequencies.

Watch out: Averaging the frequencies. The beat frequency is the difference; a 440 Hz and a 444 Hz tone beat 4 times per second.

Learn it: 14.6 Wave Interference and Standing Waves

Geometric optics

Refraction, lenses and mirrors.

Index of refraction

\displaystyle n = \frac{c}{v}

What the symbols mean

$n$: index of refraction of the material; Unit: none
$c$: speed of light in vacuum; Unit: m/s
$v$: speed of light in the material; Unit: m/s

Use it when: Use it to find how fast light travels in a material from its index, or the index from the speed.

Watch out: Getting an index below 1. Light is never faster than in vacuum, so n is always at least 1 (about 1.00 for air).

Learn it: 13.3 Refraction

Snell's law

\displaystyle n_1\sin\theta_1 = n_2\sin\theta_2

What the symbols mean

$n_1, n_2$: indexes of refraction of the first and second materials; Unit: none
$\theta_1, \theta_2$: angles of the ray in each material, measured from the normal; Unit: degrees

Use it when: Use it whenever light crosses a boundary between two materials and you need an angle or an index. Going into a higher index, light bends toward the normal.

Watch out: Measuring the angles from the surface. Measure from the normal, the line perpendicular to the surface.

Learn it: 13.3 Refraction

Thin lens and mirror equation

\displaystyle \frac{1}{s_i} + \frac{1}{s_o} = \frac{1}{f}

What the symbols mean

$s_i$: image distance from the lens or mirror; Unit: m
$s_o$: object distance from the lens or mirror; Unit: m
$f$: focal length; Unit: m

Use it when: Use it for thin lenses and curved mirrors: given two of the object distance, image distance and focal length, find the third.

Watch out: Sign errors. The focal length is positive for converging lenses and concave mirrors and negative for diverging lenses and convex mirrors, and a negative $s_i$ means a virtual image.

Try it: An object is 30 cm from a converging lens with a focal length of 10 cm. Where is the image, and how big is it compared with the object?

Answer: $\frac{1}{s_i} = \frac{1}{10} - \frac{1}{30} = \frac{2}{30}$ , so $s_i = 15\ \text{cm}$ , positive, so the image is real. Then $\lvert M \rvert = \frac{15}{30} = 0.50$ : the image is half the object's size.

Learn it: 13.2 Images Formed by Mirrors · 13.4 Images Formed by Lenses

Magnification

\displaystyle \lvert M \rvert = \left\lvert \frac{h_i}{h_o} \right\rvert = \left\lvert \frac{s_i}{s_o} \right\rvert

What the symbols mean

$M$: magnification; Unit: none
$h_i$: height of the image; Unit: m
$h_o$: height of the object; Unit: m
$s_i$: image distance; Unit: m
$s_o$: object distance; Unit: m

Use it when: Use it to find how big the image is compared with the object, from either the heights or the distances.

Watch out: Expecting this to tell you whether the image is upright. The absolute value bars hide that; work it out from a ray diagram or from whether the image is real (inverted) or virtual (upright).

Learn it: 13.2 Images Formed by Mirrors · 13.4 Images Formed by Lenses

Interference and diffraction

Path differences, single slits, double slits and gratings. The exam says the small-angle approximation is valid for single- and double-slit problems.

Path difference for constructive interference

\displaystyle \Delta D = m\lambda

What the symbols mean

$\Delta D$: difference in the distances waves travel from the two sources; Unit: m
$m$: order: 0, 1, 2, …; Unit: none
$\lambda$: wavelength; Unit: m

Use it when: Use it to decide where waves from two sources arrive in step. When the path difference is a whole number of wavelengths, you get constructive interference: loud sound or bright light.

Watch out: Using it for quiet or dark spots. Two-source destructive interference happens at half-wavelength path differences, which the sheet doesn't show.

Learn it: 14.6 Wave Interference and Standing Waves · 14.8 Double-Slit Interference and Diffraction Gratings

Path difference across a single slit

\displaystyle \Delta D = a\sin\theta

What the symbols mean

$\Delta D$: path difference between the two edges of the slit; Unit: m
$a$: width of the slit; Unit: m
$\theta$: angle from the center line to the point on the screen; Unit: degrees

Use it when: Use it for a single slit of width a. Setting it equal to $m\lambda$ with m = 1, 2, 3, … gives the angles of the dark fringes.

Watch out: Treating the single-slit condition as bright fringes. For one slit, a whole number of wavelengths across the slit gives darkness, the opposite of the double-slit rule.

Learn it: 14.7 Diffraction

Dark fringe positions for a single slit

\displaystyle a\left(\frac{y_{\text{min}}}{L}\right) \approx m\lambda

What the symbols mean

$a$: width of the slit; Unit: m
$y_{\text{min}}$: distance on the screen from the center to a dark fringe; Unit: m
$L$: distance from the slit to the screen; Unit: m
$m$: order of the dark fringe: 1, 2, 3, …; Unit: none
$\lambda$: wavelength; Unit: m

Use it when: Use it when you can measure positions on a screen: it's the single-slit dark-fringe rule with the small-angle approximation, where the sine of the angle is about y/L.

Watch out: Counting the center as a dark fringe. The middle of a single-slit pattern is the brightest spot; the first dark fringe is m = 1.

Learn it: 14.7 Diffraction

Path difference for two slits or a grating

\displaystyle \Delta D = d\sin\theta

What the symbols mean

$\Delta D$: path difference between light from neighboring slits; Unit: m
$d$: distance between the slits, center to center; Unit: m
$\theta$: angle from the center line to the point on the screen; Unit: degrees

Use it when: Use it for two slits or a diffraction grating. Setting it equal to $m\lambda$ gives the angles of the bright fringes.

Watch out: Using the slit width a for the separation d. For a grating, d is 1 divided by the number of lines per meter, so convert lines per mm or cm first.

Learn it: 14.8 Double-Slit Interference and Diffraction Gratings

Bright fringe positions for a double slit

\displaystyle d\left(\frac{y_{\text{max}}}{L}\right) \approx m\lambda

What the symbols mean

$d$: distance between the slits; Unit: m
$y_{\text{max}}$: distance on the screen from the center to a bright fringe; Unit: m
$L$: distance from the slits to the screen; Unit: m
$m$: order of the bright fringe: 0, 1, 2, …; Unit: none
$\lambda$: wavelength; Unit: m

Use it when: Use it to find where the bright fringes land on a screen behind two slits, or to work out the wavelength from measured fringe positions.

Watch out: Mixing units. Wavelengths come in nm and slit gaps in mm; convert both to meters before you divide.

Try it: Light of wavelength 600 nm passes through two slits 0.10 mm apart onto a screen 2.0 m away. How far from the center is the first bright fringe beside the central one?

Answer: With $m = 1$ : $y_{\text{max}} = \frac{m\lambda L}{d} = \frac{(600\times 10^{-9})(2.0)}{0.10\times 10^{-3}} = 0.012\ \text{m}$ , or 1.2 cm.

Learn it: 14.8 Double-Slit Interference and Diffraction Gratings

Modern physics

Photons, matter waves, blackbody radiation, the photoelectric effect, Compton scattering, mass-energy and radioactive decay.

Energy of a photon

\displaystyle E = hf

What the symbols mean

$E$: energy of one photon; Unit: J or eV
$h$: Planck's constant; Unit: J·s or eV·s
$f$: frequency of the light; Unit: Hz

Use it when: Use it for the energy of one photon of light, including photons emitted or absorbed when an atom changes energy levels. With $\lambda = \frac{c}{f}$ it becomes $E = \frac{hc}{\lambda}$ .

Watch out: Mixing joules and electron volts. Use the J·s value of h for an answer in joules and the eV·s value for an answer in eV.

Learn it: 15.1 Quantum Theory and Wave-Particle Duality · 15.3 Emission and Absorption Spectra

Wavelength from momentum

\displaystyle \lambda = \frac{h}{p}

What the symbols mean

$\lambda$: wavelength of the particle or photon; Unit: m
$h$: Planck's constant; Unit: J·s
$p$: momentum; Unit: kg·m/s

Use it when: Use it for the wavelength of a moving particle like an electron, or the momentum of a photon. For a particle, find p = mv first.

Watch out: Using the wrong mass. For an electron, use the electron mass from the constants table, not the proton mass.

Learn it: 15.1 Quantum Theory and Wave-Particle Duality

Wavelength and frequency of light

\displaystyle \lambda = \frac{c}{f}

What the symbols mean

$\lambda$: wavelength; Unit: m
$c$: speed of light in vacuum; Unit: m/s
$f$: frequency; Unit: Hz

Use it when: Use it to switch between the wavelength and frequency of light or any electromagnetic wave in vacuum.

Watch out: Using c for sound or for light inside glass or water. c is only the speed in vacuum (and nearly in air); otherwise use $\lambda = \frac{v}{f}$ .

Learn it: 14.4 Electromagnetic Waves · 15.1 Quantum Theory and Wave-Particle Duality

Peak wavelength of a blackbody

\displaystyle \lambda_{\text{max}} = \frac{b}{T}

What the symbols mean

$\lambda_{\text{max}}$: wavelength where the object gives off the most light; Unit: m
$b$: Wien's constant; Unit: m·K
$T$: absolute temperature; Unit: K

Use it when: Use it to find the wavelength where a hot object glows brightest, or its temperature from that peak, like estimating a star's surface temperature from its color.

Watch out: Using °C. T is absolute temperature in kelvin. And hotter means a shorter peak wavelength, not longer.

Learn it: 15.4 Blackbody Radiation

Power radiated by a blackbody

\displaystyle P = A\sigma T^4

What the symbols mean

$P$: power radiated; Unit: W
$A$: surface area of the object; Unit: m²
$\sigma$: Stefan-Boltzmann constant; Unit: W/(m²·K⁴)
$T$: absolute temperature; Unit: K

Use it when: Use it for the total power a hot object radiates from its surface.

Watch out: Forgetting the fourth power: doubling the temperature makes the power 16 times bigger, not 2. And T must be in kelvin.

Learn it: 15.4 Blackbody Radiation

Photoelectric effect

\displaystyle K_{\text{max}} = hf - \phi

What the symbols mean

$K_{\text{max}}$: kinetic energy of the fastest ejected electrons; Unit: J or eV
$h$: Planck's constant; Unit: J·s or eV·s
$f$: frequency of the light; Unit: Hz
$\phi$: work function, the least energy needed to free an electron from the metal; Unit: J or eV

Use it when: Use it when light knocks electrons out of a metal: the photon's energy minus the work function is the kinetic energy of the fastest electrons.

Watch out: Expecting brighter light to make faster electrons. Brighter light means more photons and more electrons; only the frequency changes the maximum kinetic energy. If the photon energy is below the work function, no electrons come out at all.

Try it: Light of wavelength 400 nm hits a metal with a work function of 2.30 eV. What is the maximum kinetic energy of the ejected electrons?

Answer: The photon energy is $E = \frac{hc}{\lambda} = \frac{1240\ \text{eV}\cdot\text{nm}}{400\ \text{nm}} = 3.10\ \text{eV}$ , so $K_{\text{max}} = 3.10 - 2.30 = 0.80\ \text{eV}$ .

Learn it: 15.5 The Photoelectric Effect

Compton shift in wavelength

\displaystyle \Delta\lambda = \frac{h}{m_e c}(1 - \cos\theta)

What the symbols mean

$\Delta\lambda$: increase in the photon's wavelength; Unit: m
$h$: Planck's constant; Unit: J·s
$m_e$: electron mass; Unit: kg
$c$: speed of light; Unit: m/s
$\theta$: angle the photon is scattered through; Unit: degrees

Use it when: Use it when a photon, usually an X-ray, bounces off an electron and you need how much longer its wavelength gets.

Watch out: Expecting the wavelength to get shorter. The photon gives some energy to the electron, so its energy drops and its wavelength gets longer.

Learn it: 15.6 Compton Scattering

Mass-energy equivalence

\displaystyle E = mc^2

What the symbols mean

$E$: energy; Unit: J
$m$: mass; Unit: kg
$c$: speed of light; Unit: m/s

Use it when: Use it to turn a mass difference into energy, as in fission, fusion and decay, where the products have slightly less mass than what you started with.

Watch out: Using a total mass instead of the mass difference. Only the missing mass becomes released energy; 1 u of it is worth 931 MeV.

Learn it: 15.7 Fission, Fusion, and Nuclear Decay

Number of nuclei left after decay

\displaystyle N = N_0 e^{-\lambda t}

What the symbols mean

$N$: number of radioactive nuclei left; Unit: none
$N_0$: starting number of nuclei; Unit: none
$\lambda$: decay constant; Unit: 1/s
$t$: time elapsed; Unit: s

Use it when: Use it to find how many radioactive nuclei remain after a time, or how long it takes to drop to a certain number.

Watch out: Mismatched time units. The decay constant and t must use the same unit, both seconds or both years. And this λ is the decay constant, not a wavelength.

Learn it: 15.7 Fission, Fusion, and Nuclear Decay

Decay constant and half-life

\displaystyle \lambda = \frac{\ln 2}{t_{1/2}}

What the symbols mean

$\lambda$: decay constant; Unit: 1/s
$t_{1/2}$: half-life, the time for half the nuclei to decay; Unit: s

Use it when: Use it to switch between half-life and decay constant. After each half-life, half of the remaining nuclei are left.

Watch out: Pressing log instead of ln. $\ln 2 \approx 0.693$ , not 0.301.

Learn it: 15.7 Fission, Fusion, and Nuclear Decay

Pages shared with another sheet

Mechanics and fluids
The Physics 2 booklet reprints the Physics 1 mechanics and fluids page, and you're expected to use it. Electric and magnetic forces go into Newton's second law, a charge moving in a magnetic field can travel in a circle with $a_c = \frac{v^2}{r}$ , and energy conservation ties kinetic energy to electric potential energy in fields and circuits.
Physics 1 equation sheet, explained →
Geometry and trigonometry
The same geometry and trig block as on the Physics 1 sheet: areas, volumes, arc length and right-triangle trig. You'll use it for things like a wire's cross-sectional area $A = \pi r^2$ and splitting fields and forces into components.
Geometry and trigonometry, explained →

Not on the sheet: know these

The exam expects you to know these without being given them.

Kirchhoff's loop rule
$\displaystyle \sum \Delta V = 0$
Around any closed loop in a circuit, the voltage gains and drops add to zero. It's how you set up equations for circuits that the series and parallel rules can't simplify.
Learn it: 11.6 Kirchhoff’s Loop Rule
Kirchhoff's junction rule
$\displaystyle \sum I_{\text{in}} = \sum I_{\text{out}}$
The current flowing into a junction equals the current flowing out, because charge is conserved. Use it with the loop rule to find the current in each branch.
Learn it: 11.7 Kirchhoff’s Junction Rule
Capacitors in steady state
A fully charged capacitor in a DC circuit carries no current, so its branch acts like a break in the wire. An uncharged capacitor, right after the switch closes, acts like a plain wire.
Learn it: 11.8 Resistor-Capacitor (RC) Circuits
Lenz's law and the right-hand rules
The sheet gives sizes, not directions. An induced current flows so that its own magnetic field opposes the change in flux, and right-hand rules give the direction of magnetic forces and of the field around a wire.
Learn it: 12.2 Magnetism and Moving Charges · 12.3 Magnetism and Current-Carrying Wires · 12.4 Electromagnetic Induction and Faraday’s Law
Critical angle for total internal reflection
$\displaystyle \sin\theta_c = \frac{n_2}{n_1}$
When light goes from a higher index to a lower index and hits the boundary at more than the critical angle, none of it gets through: it all reflects. It comes from Snell's law with the refracted angle set to 90°.
Learn it: 13.3 Refraction
Destructive interference
$\displaystyle \Delta D = \left(m + \frac{1}{2}\right)\lambda$
Two sources cancel where the path difference is a half-wavelength more than a whole number of wavelengths. That's where you find the quiet spots between two speakers and the dark fringes between double-slit bright ones.
Learn it: 14.6 Wave Interference and Standing Waves · 14.8 Double-Slit Interference and Diffraction Gratings
Standing wave wavelengths
$\displaystyle \lambda_n = \frac{2L}{n}$
For a string fixed at both ends or a pipe open at both ends, the standing waves have these wavelengths, with n = 1, 2, 3, …. For a pipe closed at one end, $\lambda_n = \frac{4L}{n}$ with only odd n.
Learn it: 14.6 Wave Interference and Standing Waves
Photon energy from energy levels
$\displaystyle E_{\text{photon}} = \lvert \Delta E \rvert$
When an atom's electron drops between energy levels it emits a photon carrying exactly the energy difference, and it can only absorb photons that match a difference. That's why spectra show sharp lines.
Learn it: 15.2 The Bohr Model of Atomic Structure · 15.3 Emission and Absorption Spectra
Conservation in nuclear reactions
In every decay, fission or fusion, the total charge and the total number of nucleons stay the same. Use that to fill in the missing particle in a nuclear equation.
Learn it: 15.7 Fission, Fusion, and Nuclear Decay · 15.8 Types of Radioactive Decay
Second law of thermodynamics
Energy flows by heating from a hotter object to a colder one on its own, never the other way, and the entropy of an isolated system never decreases.
Learn it: 9.3 Thermal Energy Transfer and Equilibrium · 9.6 Entropy and the Second Law of Thermodynamics