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Most Used Electricity Magnetism Equations

Electricity & Magnetism   Print This Page       Download This Page
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 
r2
E = k  dq 
r2
Electric Potential
V = k ∑ q
r
V = k  dq
r
Capacitance
C = Q
V
Plate Capacitor
C = κε0A
d
Cylindrical Capacitor
C = 2πκε0
ln(b/a)
Spherical Cpacitor
C =  4πκε0
(1/a) − (1/b)
Capacitive Potential Energy.
U = 1 CV2 =  1 Q2 =  1 QV
22C2
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
RpRi
Capacitors In Series
1  = ∑  1
CsCi
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 × 
r2
Solenoid
B = 0nI
Straight Wire
B = μ0I
r
Parallel Wires
FB =  μ0  I1I2
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
 
Faraday's Law
E · ds = −  dΦB
dt
∇ × E = −  B
t
Ampere's Law
B · ds = μ0ε0  dΦE + μ0I
dt
∇ × B = μ0ε0  E  + μ0 J
t
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