# Most Used Electricity Magnetism Equations

Coulomb's Law
 F = k q1q2 r2
Electric Field, Def.
 E = FE q
Electric Potential, Def.
 ΔV = ΔUE q
Field & Potential
 = − ΔV d
E = − ∇V
Electric Field
 E = k ∑ q r̂ r2
 E = k dq r̂ r2
Electric Potential
 V = k ∑ q r
 V = k dq r
Capacitance
 C = Q V
Plate Capacitor
 C = κε0A d
Cylindrical Capacitor
 C = 2πκε0ℓ ln(b/a)
Spherical Cpacitor
 C = 4πκε0 (1/a) − (1/b)
Capacitive Potential Energy.
 U = 1 CV2 = 1 Q2 = 1 QV 2 2 C 2
Electric Current
 = Δq Δt
 I = dq dt
Ohm's law
V = IR
E = ρ J
J = σE
Resitivity-Conductivity
 ρ = 1 σ
Electric Resistance
 R = ρℓ A
Electric Power
 P = VI = I2R = V2 R
Resistors In Series
Rs = ∑ Ri
Resistors In Parallel
 1 = ∑ 1 Rp Ri
Capacitors In Series
 1 = ∑ 1 Cs Ci
Capacitors In Parallel
Cp = ∑ Ci
Magnetic Force, Charge
FB = qvB sin θ
FB = q v × B
Magnetic Force, Current
FB = IB sin θ
dFB = I d × B
Biot-Savart Law
 B = μ0I ds × r̂ 4π r2
Solenoid
B = µ0nI
Straight Wire
 B = μ0I 2πr
Parallel Wires
 FB = μ0 I1I2 ℓ 2π r
Electric Flux
ΦE = EA cos θ
 ΦE = E · dA
Magnetic Flux
ΦB = BA cos θ
 ΦB = B · dA
Motional Emf
ℰ = Bv
Induced Emf
 = − ΔΦB Δt
 ℰ = − dFB dt
Gauss's Law
 ∯ E · dA = Q ε0
 ∇ · E = ρ ε0
No One's Law
 ∯ B · dA = 0
 ∇ · B = 0