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.
