# Where did the formula $Φ(x,y,z) = x^3y - z^2$ come from? How does it define a scalar field? [closed]

I want to ask that why $Φ(x,y,z) = x^3y - z^2$. I don't understand this relation? Can someone make sense of this equation.

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In what context? It looks like a potential function, and it's a scalar because all the things on the right are scalars. But without any context at all, there is no possibility to help. – tpg2114 Jan 29 at 2:41
(I am guessing this is from a homework question in electrodynamics?) This is simply a definition of some function $\Phi$. Think of it as giving a name to the expression on the RHS, simply for convenience. – David M. R. Jan 29 at 3:28

## closed as not a real question by Manishearth♦Jan 29 at 4:16

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## 1 Answer

The right hand side of your equation represents a "scalar field" in space. A scalar field is a function that has a number corresponding to each point in space.

If the x,y and z coordinates of a particular point in space is (1,2,3), then the number corresponding to that point in space, for the scalar field in your equation, is $x^3y - z^2 = 1^3*2 - 3^3 = -7$. That is, you simply substitute the coordinates of a particular point in space into the equation, and you arrive at the number corresponding to that point.

When are scalar fields used in real life? A simple example of a scalar field is temperature. That is, each point in space might have a particular temperature.

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