Electricity and magnetism/Electrostatics/The Coulomb potential produced by a charge

According to Coulomb's law, the electric field E created by a negative charge -q is the field of vectors directed towards the center of the charge whose magnitude is q/r2 where r is the distance from this center. For a positive charge q, it is the same field, except that the vectors are in opposite directions. 360px The electric field E created by an electric charge q derives from the coulomb potential V = q/r where r is the distance from the center of the charge: E = -grad V = -grad q/r The equipotential surfaces are the spheres centered on the charge. Field lines are all straight lines that extend from the center of the charge. This potential in a plane which passes through the charge can be represented by an altitude field: 640px Lines of equal altitude are equipotential lines. They are the intersections of the equipotential spheres with a plane which passes through the electric charge. -dV/dr = q/r2 = E, the length of the vector E if q is a positive charge. The Coulomb potential of an electric charge is similar to the gravitational potential of a mass: File:Gravitational field Earth lines 2.svg The lines are the field lines of the gravitational field produced by the Earth, the gravity field.