Check: by this definition, the components of e are given by E E E ar 0 0 and one can calculate the curl of e aEae a2v a2V V×E) + y 02 az dzdy (V×E)2=(V×E)2=0 Thus the curl-less e can, indeed be written as a gradient of v he scalar V(r) 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 E is not static, then generally V X E#0, so E=-VW may not hold generally