Problem $9$: $(10\%$ of Assignment Value$)$

A wire of circular cross$-$section carries current density that is not uniform but varies with distance from the center as

j$($r$)=$j$\_(0)(1-($r$^(2))/($R$^(2)))$

for radius r in the range R$=0\mathrm{.}49$mm$.$j$\_(0)$i$($r$)=0\%\_()2\_()0\%$Ij$\_(0)$r$.$

i$($r$)=$

Hint

Hints: $0\%\_($ d$)$eduction per hint. Hints remaining: $2\_()$

Feedback: $0\%$ deduction per feedback.

Part $($b$)$

If the total current in the wire is I, find an expression for the constant j$\_(0)$ in terms of the other variables in the problem$\mathrm{.}0,$ where R$=0\mathrm{.}49$mm$.$j$\_(0)$ is a constant with units of amperes per square meter.

Part $($a$)$

Find an expression for the current enclosed in a cylinder with a radius of r$.$

i$($r$)=$

Hint

Hints: $0\%\_($ d$)$eduction per hint. Hints remaining: $2\_()$

Feedback: $0\%$ deduction per feedback.

Part $($b$)$

If the total current in the wire is I, find an expression for the constant j$\_(0)$ in terms of the other variables in the problem. $\backslash [$

i$($r$)=$

$\backslash ]$

$999$ Submission$($s$)$ Remaining

Hints: $\backslash (\backslash$underline$\{0\backslash \%\}\backslash )$ deduction per hint. Hints remaining: $\backslash (\backslash$underline$\{2\}\backslash )$

Feedback: $\backslash (0\backslash \%\backslash )$ deduction per feedback.

Part $($b$)$

If the total current in the wire is $\backslash ($ I $\backslash ),$ find an expression for the constant $\backslash ($ j$\_\{0\}\backslash )$ in terms of the other variables in the problem.

Part $($c$)$

If the total current is $6\mathrm{.}5$ A $,$ what is the constant $\backslash ($ j$\_\{0\}\backslash ),$ in units of amperes per square meter?

Part $($d$)$

Find an expression for the magnetic field inside the wire, $\backslash ($ rR $\backslash ).$

Part $($f$)$

For what value of $\backslash ($ r $\backslash ),$ in meters, is the current enclosed maximum?

Part $($g$)$

What is the maximum value of the enclosed current, in units of amperes?

Part $($h$)$

For what value of $\backslash ($ r $\backslash ),$ in meters, is the magnetic field maximized?

Part $($i$)$

What is the maximum value of the magnetic field, in tesla?