Science Equations Academic Decathlon 25-26

Newton’s Law of Universal Gravitation

F_{G}=G\frac{m_1m_2}{r^2}

Coulumb's Law

F_{E}=k\frac{q_1q_2}{r^2}

Simplified Gravity Equation

F_{G}=mg

Electric Force Equation

F_{E}=qE

Strength of Electric Field Equation

E=\frac{kq}{r^2}

Gauss's Law

\phi_{E}=\frac{q}{\varepsilon_{\omicron}}

Permittivity of free space Equation

\varepsilon_{\omicron}=\frac{1}{4\pi k}

Electric Field Flux Equation

EA=\frac{q}{\varepsilon_{\omicron}}

Electric Potential Energy Equation

\Delta E=qV

Ohm's Law

I=\frac{V}{R}

Total Resistance of a Series Circuit

R_{total}=R_1+R_2+R_3+\cdot\cdot\cdot

Total Resistance of a Parallel Circuit

\frac{1}{R_{total}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\cdot\cdot\cdot

Electrical Power Equation

P=IV

Magnetic Force Equation

F_{B}=qvB

Ampere's Law (Straight Wire)

B\left(2\pi r\right)=\mu_{\omicron}I

Magnitude of Magnetic Field (Solenoid)

B=\mu_{\omicron}I\left(\frac{N}{L}\right)

Faraday's Law (Coil)

V=-N\frac{\Delta\phi_{B}}{\Delta t}

Circuit Oscillation Frequency Equation

f=\frac{1}{2\pi\sqrt{LC}}

Maxwell's Equations

\int E\cdot da=\frac{q}{\varepsilon_{\omicron}}

\int B\cdot da=0

\int E\cdot dl=\frac{d\phi_{E}}{dt}

\int B\cdot dl=\mu_{\omicron}I+\epsilon_{\omicron}\mu_{\omicron}\frac{d\phi_{E}}{dt}

Speed of Electromagnetic Waves

v=\frac{1}{\sqrt{\epsilon_{\omicron}\mu_{\omicron}}}=3\times10^8\frac{m}{s}

Velocity of wave Equation

v=\lambda f

Wavelength Equation

\lambda=\frac{c}{f}

Frequency of Wave Equation

f=\frac{c}{\lambda}

Lorentz Factor

\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}