How can gradient be zero if its a normal vector?

[aaryan0077]

Physical interpretation of gradient says that its a vector normal to equipotential (or level) surface \phi(x,y,z) = 0
but what about other surfaces, say the surface which are not equipotential?
This is my first question.

ok, now
as grad \phi is a vector normal to surface it can't 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 grad \phi is 0.
So doesn't that contradicts the assumption that grad \phi is a normal vector?

 

[kof9595995]

Equipotential surfaces are defined by the eqution:
\phi(x,y,z) = C (C is constant)
But consider the contant potential field ,say \phi(x,y,z) = 2,can you find a unique equipotential surface for it?