# What does K means in The Inverse Square Law? [closed]

Today in class i have learned the inverse square law and i was given the equation $$I=K/d^2$$ for some constant K. What does K really means?? I know that it is a constant but how can you get K or where?

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## 3 Answers

K is not a universal constant, in this context you can understand it better by changing the equation to: $$K=I*d^2$$ So for any given point source of radiation, you have that $$I*d^2$$ is a constant, it won’t be the same for all sources, but for the same source it will be same the same for any $$d$$. So the statement is that: $$I_1*d_1^2=I_2*d_2^2$$ And that’s what is used to calculate the intensity at different distances

...how can you get $$K$$ or where?

Let me briefly answer that with another question $$-$$ where can you get (your units of) $$d$$ from? That is, suppose you've observed some $$I$$. And your distance from its source is $$d$$. Then you just infer a $$K=I\times d^2$$. But if you've measured $$d$$ in meters, then you must have inferred a different $$K$$ than if you'd measured $$d$$ in feet. So, if you believe that inverse square law you've just learned, $$K$$ merely expresses the relationship between your units of intensity measurements and distance measurements, both of which are pretty arbitrary to begin with.

To somewhat remove this kind of arbitrariness, natural units (sometimes called theoretical units, like when I was taught it) can be introduced, where typically values $$c=\hbar=G=1$$ are assigned to those physical constants, and units of measurement then follow from the assigned numerical values. Lots more discussion at https://en.wikipedia.org/wiki/Natural_units

So, you could likewise just stipulate $$K=1$$ (for whatever physical field we're talking about here), and determine your units of measurement from that. It's six-of-one, half-a-dozen of the other, i.e., either specify your units beforehand and then determine $$K$$ from the ratio of your measurements, or else specify $$K$$ (usually $$=1$$) beforehand and then express your measurements in commensurate units.

It depends: your question was somewhat vague. As far as I'm concerned, inverse square laws are related to gravitational and electric forces. These can be expressed respectively as

$$\mathbf F_g = \dfrac{-G m_1 m_2}{r^2} \hat r$$ $$\mathbf F_e = \dfrac{q_1 q_2}{4 \pi \varepsilon_0} \dfrac{1}{r^2} \hat r$$

You could also consider the magnetic force, which can be expressed as

$$\mathbf F_m = \dfrac{ \mu_0 q_1 q_2}{ 4 \pi } \dfrac{1}{r^2} \mathbf R (\mathbf v_1, \mathbf v_2, \mathbf r)$$

Which is kind of an inverse square law as well.

The $$K$$ you mentioned could be any of the constants multiplying $$\dfrac{1}{r^2}$$ in those equations. In general, they relate the properties of the bodies involved in those interactions to the force each one of them feels as a consequence of the latter.