Electrostatics
No gurantee this all is correct :D
Charge:
q; SI: [C] Coulomb
Field:
E; SI: [V/m]
ε₀= 8.85x10
-12
k
vacuum
= 8.987x10
-9
Coulomb's law:
q₁ q₂
r²
F = k
1
4π ε₀ ε
k =
Electrostatic field
Point charge
F
q
E =
Distributed charge
E = ∫ dE
dq
4π ε₀ ε r²
dE=
dq
qL
;λ=
λdL
4π ε₀ ε r²
;E=∫
L
λdL
4π ε₀ ε r²
E=∫
u
L
r
Integrals are cool, but they are pain in the ass. So here are pre-calculated formulas for various shapes.
Infinite charged line's field
λ
2π ε₀ ε d
E =
where
d
is distance from the charged line, and
λ
is a charge density
Non-infinite charged line's field. Middle of line
q
2π ε₀ ε d
l² + 4d²
E =
where
d
is distance from the charged line,
l
is bar length and
q
is a charge
Ring, central axis
k λ 2π r d
(d² + r²)³ᐟ²
E =
λ r d
2ε₀ε (d² + r²)³ᐟ²
=
k q d
2ε₀ε (d² + r²)³ᐟ²
=
Where
r
is radius, and
d
is distance to the center.
Disc with a hole
E
dσ
2ε₀ε
((R₁² + d²)⁻¹ᐟ² -(R₂² + d²)⁻¹ᐟ²)
Where
R
2
is outside radius,
R
1
is inside radius, and
d
is distance to the center.
Flux:
Ф = E * S * cos α
= E * S
=∫ₛE dS