AP Physics 2 Formula Sheet: Equations by Topic, Explained

This AP Physics 2 formula sheet is a plain language guide to the equations of the second algebra based course, with Coulomb's law, $|F_E| = k\frac{|q_1q_2|}{r^2}$ , at the centre of the electricity units. The course moves beyond mechanics into heat, charge, current, magnetism, light, waves and the quantum world. It is written for study and is not the official equation sheet, which the exam board supplies with its own wording and constants table.

The physics 2 formula sheet you get in the exam lists equations; it does not say when each applies or what each symbol means in a given diagram. That is what this page adds. US symbols are used: $s_o$ and $s_i$ for object and image distance, with real images positive. If you are coming straight from the first course, the AP Physics 1 sheet covers the mechanics you will still need, and the AP physics formula sheet hub lists every course.

Quick facts

What this is
A study guide, not the exam board's sheet
Math level
Algebra and trigonometry
Most used
$\Delta V = IR$ and $F_E = k\frac{|q_1q_2|}{r^2}$
Big topics
Thermodynamics, electricity, magnetism, optics, waves, modern physics
Optics signs
Real image distances positive, virtual negative
Coulomb constant
k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m²/C²

Thermodynamics and gases

Gas laws, internal energy and heat flow
Equation	Meaning	SI unit	Study page
$PV = nRT = Nk_BT$	ideal gas law, by moles or by molecules	Pa m³ = J	Thermodynamics
$K_{avg} = \frac{3}{2}k_BT$	average translational kinetic energy per molecule	J	Thermodynamics
$\Delta U = Q + W$	first law, with W the work done on the gas	J	First law
$W = -P\Delta V$	work done on a gas at constant pressure	J	First law
$\frac{Q}{\Delta t} = \frac{kA\,\Delta T}{L}$	conduction through a slab, joules per second	W	Thermal conductivity

Sign conventions differ. AP writes ΔU = Q + W with W done on the gas; many Indian books write ΔU = Q − W with W done by the gas. Both describe the same physics.

Electric force, field and potential

Electrostatics
Equation	Meaning	SI unit	Study page
$\|F_E\| = k\frac{\|q_1q_2\|}{r^2}$	force between point charges (Coulomb's law)	N	Electrostatic force
$\vec{E} = \frac{\vec{F}_E}{q}$	field as force per unit test charge	N/C	Electric field
$\|E\| = k\frac{\|q\|}{r^2}$	field around a point charge	N/C	Electric field
$V = k\frac{q}{r}$	potential near a point charge	V	Voltage
$U_E = k\frac{q_1q_2}{r}$	potential energy of a charge pair	J	Electrostatic force
$\|E\| = \frac{\|\Delta V\|}{\|\Delta r\|}$	uniform field from potential difference	V/m	Electric field
$C = \kappa\varepsilon_0\frac{A}{d}$	parallel plate capacitance	F	Capacitance
$U_C = \frac{1}{2}Q\Delta V = \frac{1}{2}C(\Delta V)^2$	energy held by a capacitor	J	Capacitance

Force and field are vectors, so add them with components. Potential and potential energy are scalars, so add them with signs. Gravity and electricity share the same inverse square shape, which is why the field and potential ideas from gravitation carry over.

Circuits

Current, resistance and networks
Equation	Meaning	SI unit	Study page
$I = \frac{\Delta q}{\Delta t}$	current as charge per second	A	Current
$R = \frac{\rho\ell}{A}$	resistance of a wire	Ω	Resistivity
$\Delta V = IR$	Ohm's law for a resistor	V	Ohm's law
$P = I\Delta V$	power delivered to a component	W	Resistance
$R_s = \sum R_i,\ \frac{1}{R_p} = \sum \frac{1}{R_i}$	series and parallel resistors	Ω	Resistance
$C_p = \sum C_i,\ \frac{1}{C_s} = \sum \frac{1}{C_i}$	capacitors combine the other way round	F	Capacitance

Example: a mixed circuit

A 12 V battery drives a 4.0 Ω resistor in series with a pair of resistors, 6.0 Ω and 3.0 Ω, connected in parallel. Find the current from the battery and the current in the 3.0 Ω resistor.

Parallel pair: $\frac{1}{R_p} = \frac{1}{6.0} + \frac{1}{3.0} = \frac{1}{2.0}$ , so $R_p = 2.0\ \Omega$ . Total: $4.0 + 2.0 = 6.0\ \Omega$ .

Battery current: $I = \frac{12}{6.0} = 2.0\ \text{A}$ . Voltage across the pair: $(2.0)(2.0) = 4.0\ \text{V}$ .

Current in 3.0 Ω: $\frac{4.0}{3.0} = 1.3\ \text{A}$ (and 0.67 A in the 6.0 Ω). Check: 1.33 + 0.67 = 2.0 A.

Magnetism and electromagnetic induction

Magnetic forces, fields and flux
Equation	Meaning	SI unit	Study page
$\|F_B\| = \|q\vec{v}\|\|\vec{B}\|\sin\theta$	force on a moving charge	N	Magnetic force
$\|F_B\| = \|I\vec{\ell}\|\|\vec{B}\|\sin\theta$	force on a current carrying wire	N	Magnetic force
$B = \frac{\mu_0 I}{2\pi r}$	field around a long straight wire	T	Magnetic field
$\Phi_B = BA\cos\theta$	magnetic flux through a loop	Wb	Magnetic flux
$\varepsilon = -\frac{\Delta\Phi_B}{\Delta t}$	induced emf (Faraday's law, sign from Lenz's law)	V	Electromotive force
$\varepsilon = B\ell v$	emf of a rod sliding through a field	V	Electromotive force

Use the right hand rule for direction; the formula gives only the size. A charge moving parallel to the field feels no magnetic force.

Optics and waves

Light, lenses and interference
Equation	Meaning	SI unit	Study page
$n = \frac{c}{v}$	index of refraction	no unit	Index of refraction
$n_1\sin\theta_1 = n_2\sin\theta_2$	refraction at a boundary (Snell's law)	no unit	Index of refraction
$\frac{1}{s_i} + \frac{1}{s_o} = \frac{1}{f}$	thin lens and mirror equation	m⁻¹	Lens formula
$\|M\| = \left\|\frac{h_i}{h_o}\right\| = \left\|\frac{s_i}{s_o}\right\|$	size of the magnification	no unit	Magnification
$v = f\lambda$	wave speed	m/s	Wave velocity
$d\sin\theta = m\lambda$	bright fringes from a double slit or grating	m	Wavelength

Example: a converging lens

An object stands 30 cm from a converging lens of focal length 10 cm. Where is the image and what is the magnification?

$\frac{1}{s_i} = \frac{1}{10} - \frac{1}{30} = \frac{2}{30}$ , so $s_i = 15\ \text{cm}$ (positive, so real).

$M = -\frac{s_i}{s_o} = -\frac{15}{30} = -0.50$ . The image is real, inverted and half the size. In NCERT sign convention you would write u = −30 cm and get v = +15 cm, the same image.

Modern physics

Photons, matter waves and mass energy
Equation	Meaning	SI unit	Study page
$E = hf$	energy of a photon	J	Photons and matter waves
$K_{max} = hf - \phi$	photoelectric effect	J	Work function
$\lambda = \frac{h}{p}$	de Broglie wavelength	m	Wavelength
$E = mc^2$	rest energy, used for mass defect	J	Relativity

Work in electronvolts for atomic energy levels: a photon emitted when an electron drops between levels carries exactly the energy difference.

Using an ap physics 2 formula sheet without losing marks

Learn the conditions. Ohm's law fits ohmic resistors; the lens equation assumes thin lenses and small angles.
Explain with words, not only symbols. Many free response parts ask you to justify a claim. Quote the relation, then say what changes and why.
Practise with the real sheet. Download the current version from the exam board and use it on every practice set.
Watch powers of ten. μC, nF and nm turn up in every topic.

For the calculus versions of these ideas, see the AP Physics C E&M sheet.

Frequently asked questions

Is this page the exam board's own AP Physics 2 sheet?

No. This is a study guide. The exam board provides the official equation sheet and constants table for the exam, so practise with that version as well.

What topics does the physics 2 formula sheet cover?

In general terms: thermodynamics, electric force, field and potential, circuits, magnetism and induction, geometric and physical optics, waves, and modern physics. Check your current course outline for the exact list.

What is the difference between AP Physics 2 and AP Physics C E&M?

Both cover electricity and magnetism, but AP Physics 2 uses algebra and also includes heat, optics and modern physics. AP Physics C E&M goes deeper into fields using calculus.

Which sign convention does AP Physics 2 use for lenses?

Distances to real images and real objects are positive, and virtual image distances are negative. Converging lenses take a positive f, diverging lenses a negative f.

Do I still need to memorise formulas for AP Physics 2?

You need fewer, but you must know what every symbol means and when each equation applies. Definitions such as current, resistance and flux should come to you without looking.