Introductory Physics Volume Two

1.9 Summary 35
§ 1.9 Summary
Definitions
Electric Field:
Electric Flux:
⃗E = ⃗ F a
q a
dφ e = E ⃗ · dA ⃗
∫
φ e = ⃗E · dA ⃗
Facts
Coulomb’s Law
⃗F ab = 1 ˆr ab
q a q b
4πɛ 0 rab
2 = 1 ⃗r ab
q a q b
4πɛ 0 rab
3
Theorems
Electric Field of a Point Charge:
⃗E(⃗r) = 1 q ⃗r − ⃗r s
4πɛ 0 |⃗r − ⃗r s | 3
where ⃗r points to the field point and ⃗r s points to the charge q.
Electric Field of a Distribution of Charge:
⃗E(⃗r) = 1 ∫
dq ⃗r − ⃗r s
4πɛ 0 |⃗r − ⃗r s | 3
where ⃗r points to the field point and ⃗r s points to the charge element
dq.
Gauss’ Law: ∮
⃗E · dA ⃗ = Q in
ɛ 0
Superposition Theorem: If a charge distribution ρ 1 produces an
electric field ⃗ E 1 and the charge distribution ρ 2 produces an electric
field ⃗ E 2 then if both charge distributions are present the electric field
is ⃗ E = ⃗ E 1 + ⃗ E 2 .