Week 4

Basic Facts

Electric Flux: The flux Φ of an electric field E through a surface S is given by the integral
Φ = ∫E^.ds where the integral is over the surface S.

Gauss's Law for the Electric Field: The net flus through a closed surface S is proportional to the total charge Q enclosed by the surface.

∫ E^.ds = Q
              ε₀

The Electric field inside a closed spherical shell of charge is exactly 0.

The electric field outside a spherically symmetric ball of charge is the same as if all the charge were concentrated in a point at the centre of the sphere.

NOTE: The charge does NOT have to be uniformly distributed; it must simply depend only on r and not on the angles.

The electric field in a region entirely surrounded by a conductor is exactly zero unless there are other charges in that region.

Useful Facts

The electrostatic potential V a distance r>>d from a dipole made from charges Q separated by d is given by

 

Useful Facts

The field from an infinite straight line of charge with density λ Coulombs/metre depends only on the perpendicular distance ρ from the line has magnitude
E = __λ____
       2πε₀ |ρ|
and points perpendicularly outwards (or inwards) from the line.

The field from an infinite flat sheet of charge of density σ points away from the sheet and has magnitude
E = σ  independent of the distance from the sheet.
       2ε₀

The electric field E very near the surface of a conductor is perpendicular to the surface and causes (or is caused by) a local charge density σ where
E = σ .
       ε₀