Circuits

Magnetic field of a loop of wire: B = µ₀ I / 2 R

Time rate of electric field on a capacitor: dE/dt = I / ( ε₀ A )
(where A is the area of a capacitor plate)

Electric field between capacitor with a charge: E = Q / ( ε₀ A )

For positive charges, F and E are opposite.

For negative charges, F and E are the same direction.

Potential energy between two charges: U = k q₁ q₂ / r₁₂²

Θ = q_enclosed / ε₀

For an infinite line: q_enclosed = λ L and E = 2 k λ / r

For a sheet: E = ½ σ / ε₀

For two plates: E = - V / d (ΔV between plates, divided by distance between plates)

For a circle: E = k q / r²

Cylindrical air coil: L (inductance) = µ₀ N² A / l

ΔV = I R = E d

ΔU = q ΔV for some test charge

Q = C V = ε₀ A E

W = ΔU = - q ΔV

ΔV = ΔU / q = k q / r

℘ = I² R = I ΔV = ΔV² / R = I Ε

Ε = I R + I r (way to find epsilon when an external resistor is in the circuit)

R is external resistance, r is internal battery resistance

ΔV = Ε - I r

I = Ε / ( R + r)

Epsilon is EMF, the Delta V when no resistor is in place if you will, and delta V is the voltage difference when the resistor is connected.