In the Coulomb gauge, this is the volume integral 
In the Coulomb gauge, this is the volume integral of charge density over distance, so its nth spherical moment falls off as one over distance to the n; thus, this field for a dipole falls off as one over distance squared. The negative gradient of this quantity is the static electric field. Half the volume integral of this times the charge density is the energy needed to assemble a charge distribution because this scalar field is the energy required to bring a unit charge to a point. For 10 points, name this electromagnetic scalar field that can be understood as the amount of the namesake type of energy per unit charge and that has unit volt.
In the Coulomb gauge, this is the volume integral of charge density over distance, so its nth spherical moment falls off as one over distance to the n; thus, this field for a dipole falls off as one over distance squared.
scalar {potential} [grudgingly accept {voltage}; prompt on {V}; prompt on {phi}]