Question

when we say a varies inversely with b...

Answer 1

It means that as b increases, a decreases, and vice-versa.

Answer 2

how would I write that symbol in latex?

Answer 3

\[a \alpha \frac{ 1 }{ b }\]

Answer 4

The alpha symbol is a bit close to the a, but it's about the best I could do.

Answer 5

You can write it as
\[a=\frac{k}{b}\]
where k is a constant of proportionality.

Answer 6

so this statement: The electrostatic force varies inversely with the square of their separation distance

means:
\[F \;\;\;\alpha \;\;\;\;r^2\]

correct?

Answer 7

No, that's directly proportional. Needs to be 1/r^2

Answer 8

```
\proto
```
\[\propto\]

Answer 9

@UnkleRhaukus looks like it's propto not proto
\[F \propto \frac{ 1 }{r^2 }\]

Answer 10

*

```
\propto
```
\[\propto\]

Answer 11

Makes sense. Thanks everyone!

Answer 12

The electrostatic force varies inversely with the square of their separation distance\[\mathbf{\vec F}\propto \frac1{r^2}\quad\implies\quad\mathbf{\vec F}= \frac k {r^2}\]

Answer 13

btw \[F \;\;\;\alpha \;\;\;\;r^2 \] would mean that the electrostatic force varies directly with the square of the distance, ie as the distance increases, force increases - which we know is not true.