ch 6 gauss's law and flux L5 and L6

gauss’s law helps

calculate E-field when source charge distribution has some spatial symmetry

electric flux

how many lines penetrate an area, magnitude of E-field times surface area perpendicular to field lines

Φ_E =

dot product of electric field (N/C) and surface area (m²)

direction of area vector for open surface

either up or down normal to surface

direction of area vector for closed surface

points from inside of closed space to outside

surface integral definition

Φ_E = ∫ E • dA, dA is infinitesmal, approximately flat with uniform field

e-flux through closed surface

vectors ΔA point in different directions, but perpendicular to surface at each point; we compute dot product of E and ΔA at each piece and add them up

net flux through surface is

proportional to net number of lines leaving (# leaving - # entering)

for any empty closed surface, net flux is

zero (lines in = lines out

flux of point charge

that of a spherical surface surrounding q, determined by the charge q surrounded by the surface and no outside charge

flux is the same independent of

radius or shape of closed surface

if net enclosed charge is zero (e.g. one positive and one negative), then net flux is

also zero

gauss’s law for any closed surface

∫ E • dA = q_in/ε₀

choose Gaussian surface such that

E is a constant on the surface, E is perpendicular to da, or E is parallel to dA

electric field outside uniform sphere

E = 1/4πε₀ Q/r² r^

electric field inside uniform sphere

E = 1/4πε₀ Qr/R³ r^