q is proportional to

of lines

flux

Flux is a scalar quanity that provides a quantitative measure for the # of field lines crossing a surface. Flux is the measure of the exposure of the area to the electric field.

Flux for a uniform E field

Øe = E dot A

A (area vector)

The area vector is the vector perpendicular to the surface with the magnitude A.

Flux is proportional to

the # of field lines piercing surface

E is proportional to

Line density

line density equals

the # of field lines/A

EA is proportional to

the number of field lines

hypothetical surface

imaginary closed surface

E in a nonuniform electric field surface

E varies over the entire surface, in both magnitude and direction

Typical calculus manoeuvre to resolve the problem of calculating flux of a nonuniform electric field.

Subdivide the surface area into many smaller areas over which E varies only slightly.

Gaussian Surface

Hypothetical Closed 3D surface

Surface area of sphere formula

A = 4πr^2

Gauss’ Law

Øe = ∫E • dA = qenclosed/εnaught

Spherical Symmetry

Constant r, so electric field is the same on all points of the surface.

η

Surface Charge Density (eta)

Surface Charge Density formula

η = Q/A = qen/A

Inside a sphere conductor, the electric field

The electric field is 0. No net charges.