EM Quiz 1

Line integral

∫v*dl, from vectors a to b

Surface integral

∫v*da over a surface S

Volume integral

∫Tdt over volume V with T as a scalar function

Fundamental theorem for gradients

∫(delT)*dl = T(b)-T(a)

Divergence theorem/Gauss’ Law

∫del*Adt = ∫°vda

Fundamental theorem of curls/Stokes

∫(del*f)*da = ∫°f*dl

Field E of a point charge

E = q/4piεr² r

According to the Helmholtz theorem, every vector field is specified by…

The curl, divergence, and boundary conditions

Equation 2.8/Coulomb’s law

E(r ) = 1/4piε∫p(r’)/(script r)² (script r) dt’

[E]

N/C = force/charge

[linear charge density]

charge/length = C/m

Maxwell 1 - differential form

del*E = p/ε

In units, del adds a term of

1/length

Maxwell 1 integral form

∫°E*da = Qencl/ε = flux of E

Maxwell 2

del x E = 0 for statics

Field from potential

E = -delV

Principal of superposition

The total field is just a sum of the individual fields

Poisson’s equation

-del²V = p/ε

Laplace’s equation

-del²V = 0

Force on a point charge q

F = qE