What is the meaning of squaring a number

[Ross J]

Yes, I understand it means a value times itself. I want to know WHY you do it though, what is the physical meaning behind it.

For example in nuclear physics for a potential force,

V = Ze^2 / r

Where e is the electric charge unit, Z is the atomic number, and r is radius. Why is it squared? What is this telling me?

 

[russ_watters]

Welcome to PF!

Yes, I understand it means a value times itself.

That's really all there is to it.

I want to know WHY you do it though, what is the physical meaning behind it.

For example in nuclear physics for a potential force,

V = Ze^2 / r

Where e is the electric charge unit, Z is the atomic number, and r is radius. Why is it squared? What is this telling me?

Every equation is different and while some share common reasons for doing things, there are many different reasons why an equation might include squaring something. There is no one answer because there really isn't anything to this other than the first answer you already know. It's not any more profound than why sometimes you add, subtract, multiply or divide. Knowing why that equation is what it is doesn't really provide an additional answer to the original question beyond the one you already know.

But the derivation of that equation can be found here:
http://dev.physicslab.org/Document.aspx?doctype=3&filename=AtomicNuclear_BohrModelDerivation.xml

In short, you're multiplying the charge of the proton(s) by the charge of the electon.

 

[Ross J]

Thank you, that was more than I could have hoped for

 

[sophiecentaur]

Yes, I understand it means a value times itself. I want to know WHY you do it though, what is the physical meaning behind it.

For example in nuclear physics for a potential force,

V = Ze^2 / r

Where e is the electric charge unit, Z is the atomic number, and r is radius. Why is it squared? What is this telling me?

That question is about how Maths seems to model the Physical World so well. After all, Maths is just 'in our heads'. Considering the nature of Mathematics can make your brain ache.

 

[QuantumPion]

When you square something, you are turning a single dimension (length) into an area. Many physical quantities are integrals (the area under the curve) of some other quantity. For example, the kinetic energy = ½ m v² is the integral of force times velocity ∫ F⋅v dt which goes to the fundamental definition of energy.