Physical interpretation of gradient says that its a vector normal to equipotential (or level) surface [tex]\phi(x,y,z) = 0[/tex] but what about other surfaces, say the surface which are not equipotential? This is my first question. ok, now as [tex]grad \phi[/tex] is a vector normal to surface it cant be 0. Because that would mean that surface have no normal vector, or say a normal vector of indeterminate direction (as 0 vector is of indeterminate direction). how can it be possible that a surface has no normal vector, more specifically a 0 vector as its normal vector? But I have seen many examples in which [tex]grad \phi[/tex] is 0. So doesn't that contradicts the assumption that [tex]grad \phi[/tex] is a normal vector?