Proportionality relationship and how to convert using it

[rwooduk]

Homework Statement

Homework Equations

Please see below.

3. The Attempt at a Solution

The idea is to find B_min. We know: $$
\tau \frac{eB}{m}\gg 1 \\ \\

\rightarrow \frac{eB}{m}\gg \tau$$

Points:

[1] We are given $$\tau \propto \frac{1}{T^{2}}$$ .

[2] We are also given a conversion factor $$\tau =10ns \ at \ 1K$$.

Now, how would you use [1] and [2] to convert 300K?

I'm assuming you can't just use [2] and do $$300K\cdot \frac{10ns}{1K} = 3X10^{-7}s$$ because of the non-linear relation given in [1].

Am I just confusing things?

 

[pasmith]

You are told that $\tau = CT^{-2}$ for some constant $C$, and are given sufficient information to determine $C$.

 

[rwooduk]

You are told that $\tau = CT^{-2}$ for some constant $C$, and are given sufficient information to determine $C$.

Ahhh, don't know why I didn't think of it like that! Many thanks!