# How can gradient be zero if its a normal vector?

1. Jul 5, 2009

### 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 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 $$grad \phi$$ is 0.
So doesn't that contradicts the assumption that $$grad \phi$$ is a normal vector?

2. Jul 5, 2009

### 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?