Electrostatics

The fundamental equations of electrostatics are linear equations,

 (SI units),         (Gaussian units).

The principle of superposition holds.

The electrostatic force on a particle with charge q at position r  is F=qE(r).

. 

f is the electrostatic potential.

Important formulas:

The field at r due to a point charge at r’:   

(Omit the factor to obtain the corresponding expressions in Gaussian units.)

The field of a charge distribution:

(We consider volume, surface, and line charge distributions and point charges.)

The potential at r due to a point charge at r’:     

The potential of a charge distribution:

Gauss’ law:

(SI units),    (Gaussian units).

In situations with enough symmetry, Gauss’ law alone can be used to find E.

The electrostatic energy of a charge distribution:

or, for a continuous charge distribution,

(SI units),      (Gaussian units).

Dipoles

The field of a dipole at the origin:

The potential of a dipole at the origin:

The force on a dipole:

The torque on a dipole:

The energy of a dipole in an external field:

Properties of conductors in electrostatics

Dielectrics

The polarization     is defined as the dipole moment per unit volume.

The total charge density is due to free and to bound (polarization) charges.

.

(SI units),                          (Gaussian units).

For linear, isotropic, homogeneous (lih) dielectrics we have

,                                            ,

,             ,

,              .

Boundary conditions in electrostatics