_{0 }) = 8.99 x 10

^{9 }N m

^{2 }/ C

^{2 }

k is the proportionality constant in Coulomb's law, and is sometimes known as Coulomb's constant.

ε

ε

_{0 }= 8.85 x 10^{-12 }C^{2 }/ Nm^{2 }ε

_{0 }is a constant known as the permittivity of free space, which is the absolute value of the dielectric permittivity of a vacuum.
F

Coulomb force law, inverse square law between objects 1 and 2 with a given charge a s a function of distance squared. Can be both attractive and repulsive in nature.

_{ 12 }= (k Q_{1 }Q_{2 })/ r^{2 }_{12}Coulomb force law, inverse square law between objects 1 and 2 with a given charge a s a function of distance squared. Can be both attractive and repulsive in nature.

E = Q r / (4 π ε

Electric field due to a point charge, written with ε

_{0 }r^{2 })Electric field due to a point charge, written with ε

_{0 }as opposed to using constant k.
Dipole field

E = [3 ( p . r ) r - p] / (4 π ε

_{0 }r^{3 }) - [p δ^{3 }(r)] / (3 ε_{0 })
In one direction along or perpendicular to dipole axis

E = p / (2 π ε

_{0 }x^{3 })
Energy and Torque on a dipole in an external E-field

U = - p . E , τ = p x E

Electric field of infinite line of charge:

E = λ / (2 π ε

Where λ is defined as the charge per unit length.

E = λ / (2 π ε

_{0 }r)Where λ is defined as the charge per unit length.

Electric field of infinite charged plane:

E = σ / (2 ε

Where σ is defined as the charge per unit area.

E = σ / (2 ε

_{0 })Where σ is defined as the charge per unit area.

Electric field of ring along axis:

E = Q x / [ 2 π ε

E = Q x / [ 2 π ε

_{0 }r (x^{2 }+ a^{2 })^{3/2 }]
Electric field of disk along axis

E = σ / 2 ε

E = σ / 2 ε

_{0 }[ 1 - z / (z^{2 }+ R^{2 })^{1/2 }]
Electric flux:

Φ = E . A ;

dΦ = E . dA ; Φ = ∫ E . dA

Φ = E . A ;

dΦ = E . dA ; Φ = ∫ E . dA

Gauss's Law:

§ E . dA = Q

_{enc }/ ε_{0}
Potential energy

U

V

E

U

_{ab }= U_{b }- U_{a }= -W_{ab }= - ∫ F . dl ;V

_{ab }= V_{b }- V_{a }= - ∫ E . dl ; V = k Q / r ; V = k ∫ dq / r ; E_{l }= - dV / dlE

_{x }= - dV / dxU

_{12 }= k Q_{1 }Q_{2 }/ r_{12}
Capacitors

Q = C V

Parallel plate

Q = ε

U = Q

C = K C

ε = K ε

C = C

1/C = 1/C2 + 1/C3

_{0 }A / dU = Q

^{2 }/ 2 CC = K C

_{0 }ε = K ε

_{0 }C = C

_{1 }+ C_{2 }1/C = 1/C2 + 1/C3

Ohm's law

I = V/R = Δ Q / Δ t

Resistivity

ρ = ρ

_{0 }[ 1 + α (T - T_{0 })]
Power

P = VI = V

The basic relation P = VI was transformed to the other two states by using Ohm's law.

^{2 }/ R = I^{2 }RThe basic relation P = VI was transformed to the other two states by using Ohm's law.

Alternating Current

V = V

P = V

P

_{0 }sin ω tP = V

^{2 }_{0 }sin^{2 }(ω t) / RP

_{avg }= V^{2 }_{0 }/ (2 R)
Current density

j = I/A = n e v

e = -1.6 x 10

_{drift }= E / ρe = -1.6 x 10

^{-19 }C
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