Light and Maxwell's Equations

Divergence of E

∇∙E=ρ/ε₀
Field Lines can leave and never return from the source. Implies that charges can be solely negative or positive - unlike magnets where there are two poles.

Divergence of B

∇∙B=0
Means that there is no monopole for magnets. The magnetic field lines that leave must come back.

Electromagnetic Induction

The process of creating a current in a circuit by changing a magnetic field
∇×B ⃗=μ₀ J ⃗

Faraday's Law

Faraday's law states that the magnitude of an induced e.m.f. is proportional to the rate of change of flux linkage.

ε = -(dφ/dt)

ε is the induced e.m.f. in V
dφ is the change of magnetic flux in Wb
dt is the time taken in s

Lenz's Law

The polarity of the induced e.m.f. tends to produce a current that creates a magnetic flux to oppose the original change in magnetic flux through the area enclosed by the current loop.
ε = -(dφ/dt)=-(d/dt) ∫B.da

I.e. The direction of an induced current always opposes the change that produced it.

2nd Maxwell's equation for dynamic fields

∇×E=-∂B/∂t
Differential form of Faraday's Law

Electric field generation

Anywhere there is a changing magnetic flux.
Or rather when there is a time varying magnetic field.

Angle between E and B

The angle is normal since B is the vector product of the two vectors ∇ and E

Integral Form: ∮E.da = Q/ε₀
Gauss' Law for E

Differential Form: ∇.E ⃗ = (1/ε₀) ρ

Integral Form: ∮E.dl = 0
E is Conservative

Differential Form: ∇×E ⃗ = 0

Integral Form: ∮B.dl = μ₀I
Ampere's Law

Differential Form: ∇×B ⃗ = μ₀I

Integral Form: ∮B.da = 0
Gauss' Law for B

Differential Form: ∇.B ⃗ = 0