How can gradient be zero if its a normal vector?

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  • #1
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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?
 

Answers and Replies

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

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