Check: by this definition the components of e are given by E E E ax 2 and one can calculate the curl of e 0E,0E a2v a2V (V×E) + 02 y02a20 sImilarly, V×Ey=(V×E)2=0 Thus the curl- less e can, indeed be written as a gradient of v The scalar Vir is called the electric potential Remarks (1) The minus sign in E=-VV implies that the electric field E points toward a decrease of V(r) (2)V is fixed only up to an arbitrary constant: V=V+C (3)If is not static, then generally VXE+0, so E=-VV may not hold generally