Electrical and Magnetic Properties $[20$ pts total$]$

A plain carbon steel wire $0\mathrm{.}2$ cm in radius is to offer a resistance of no more than $15$ at room temperature. If the electrical conductivity $$ of the steel at this temperature is $0\mathrm{.}65{10}^7(-m{)}^{-1},$ calculate the maximum wire length. $(3$ pts $)$

$R_0$

$($:$\frac{1}{(\frac{1}{i}m{)}^{-1}}\})$

Maximum wire length $306\mathrm{.}71q,$

b$)$ The electrical conductivity of the above carbon steel wire decreases by an order of magnitude to $0\mathrm{.}65{10}^6(-m{)}^{-1}$ after going through certain postreatment processes. Please find at least two posttreatment processes that may induce such a change of electrical properties, justify your choices using concise and reasonable explanations. $(3$ pts$)$