Aca Deca (2025-2026) - Science - Equations

Equations in the 2025-2026 Aca Deca Science resource guide

Ampere's law

B (2𝝅r) = μ₀ I
I = current passing through the Amperian loop
B = magnetic field
2𝝅r = length around the Amperian loop
μ₀ = permeability of free space

Coulomb constant

8.99 x 10⁹ N m²/C²

Coulomb's law

Fᴇ = k ( q₁q₂ / r² )
q = amount of charge of the two objects
r = distance between them
k = Coulomb constant
Electrical force
Inverse square law

Electric field

E = σ / 2ε₀
σ = surface charge density

Electric Field

Fᴇ = qE

Faraday's Law

V = -N ( ∆Φʙ / ∆t )
Φʙ = magnetic field flux
N = amount of loops
∆ = change in quantity

Frequency

f = c / λ
c = speed of light
λ = wavelength

Gauss's law

Φᴇ = q / ε₀
Amount of electric field that passes through a Gaussian surface
ε₀ = permittivity of free space
Φ = "phi", electric field flux

Gravitational Field

Fɢ = mg

Gravitational Force

Fɢ = G ( m₁m₂ / r² )

m = masses of the two objects
r = distance between them
G = gravitational constant / Newton's constant

Kinetic energy of a particle

∆E = q x V
V = voltage (change in height of a ball)
q = charge (weight of a ball)

Lorentz factor

γ = 1 / √ (1 - v²/c²)
The effects of relativity

Magnetic field in a Solenoid

B = μ₀ I (N/L)
L = length of solenoid
N = number of loops

Magnetic Force

Fᵦ = q v B
q = electric charge of the particle experiencing the force
B = strength of the magnetic field (measured in teslas)
v = velocity of the particle

Maxwell's 1st equation

How an electric field is created around charge
Full mathematical form of Gauss's law

Maxwell's 2nd equation

How a magnetic field is created around charge

Maxwell's 3rd equation

Faraday’s law

A changing magnetic field gives rise to an electric field

Maxwell's 4th equation

The changing electric field between the plates of a discharging capacitor

Newton's constant

6.67 x 10⁻¹¹ N m²/kg²

Ohm's Law

I = V/R
V = voltage
I = Current
R = resistance, measured in ohms (Ω)
Current in a circuit

Oscillating circuit

f = 1 / (2𝝅 √LC)
C = capacitance of the capacitor
L = inductance of the inductor

Resistance of a Parallel Circuit

1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + 1/R₃ + …

Resistance of a Series Circuit

Rₜₒₜₐₗ = R₁ + R₂ + R₃ + …

Speed of Light

c = ( 1 / √ ε₀μ₀ ) = 3 x 10⁸ m/s

Strength of proton's electric field

E = kq / r²

Velocity of a wave

v = λf
λ = wavelength
f = frequency

Wavelength

λ = c / f
c = speed of light
f = frequency

ε₀

1 / 4𝝅k
Permittivity of free space