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

$j(r)=A(1-\frac{r}{R}),$

where $R$ is the radius of the wire and $r$ varies in the range $AR=0\mathrm{.}37$mmi$(r)=A2(\frac{3r^{2}R-2r^3}{6R})IAA=\frac{\text{I}}{2\frac{3R^2-2R^2}{6}}$vAA$=6\mathrm{.}63**{10}^7$

$A=6\mathrm{.}630{10}^7\frac{A}{m^2}IB(r)=$

${}_{0}2(\frac{\text{I}}{2\frac{3R^2-2R^2}{6}})\frac{\frac{3r^{2}R-2r^3}{6R}}{2r}$

Correct! $r>RB(r)={}_0\frac{\text{I}}{2r},$ Correct! $rrr,in$ terms $of$ the current I.

$B(r)=$

${}_{0}2(\frac{\text{I}}{2\frac{3R^2-2R^2}{6}})\frac{\frac{3r^{2}R-2r^3}{6R}}{2r}$

Correct!

Part $(e)$

Find $an$ expression for the magnetic field outside $of$ the wire. That $is,$ for $r>R.$

$B(r)={}_0\frac{\text{I}}{2r},$ Correct!

Part $(f)$

For what $r,in$ 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 $ofr,in$ meters, $is$ the magnetic field maximized?

Part $(i)$

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

Grade Summaryr.

$i(r)=A2(\frac{3r^{2}R-2r^3}{6R})$

Correct!

Part $(b)$

$If$ the total current $in$ the wire $is$ I, find $an$ expression for the constant $A,in$ terms $of$ the other variables $in$ the problem.

$A=\frac{\text{I}}{2\frac{3R^2-2R^2}{6}}$

Correct!

Part $(c)v$

$If$ the total current $is9\mathrm{.}5A,$ what $is$ the value $of$ the constant $A,in$ units $of$ amperes per square meter?

$A=6\mathrm{.}63**{10}^7$

$A=6\mathrm{.}630{10}^7\frac{A}{m^2}$

Correct!

Part $(d)$

Find $an$ expression for the magnetic field inside the wire, $r,in$ terms $of$ the current I.

$B(r)=$

${}_{0}2(\frac{\text{I}}{2\frac{3R^2-2R^2}{6}})\frac{\frac{3r^{2}R-2r^3}{6R}}{2r}$

Correct!

Part $(e)$

Find $an$ expression for the magnetic field outside $of$ the wire. That $is,$ for $r>R.$

$B(r)={}_0\frac{\text{I}}{2r},$ Correct!

Part $(f)$

For what $r,in$ 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 $ofr,in$ meters, $is$ the magnetic field maximized?

Part $(i)$

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

Grade Summary$0.$ Here, $Ais$ a constant with units amperes per square meter, and the radius $of$ the wire $isR=0\mathrm{.}37mm.$

Part $(a)$

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

$i(r)=A2(\frac{3r^{2}R-2r^3}{6R})$

Correct!

Part $(b)$

$If$ the total current $in$ the wire $is$ I, find $an$ expression for the constant $A,in$ terms $of$ the other variables $in$ the problem.

$A=\frac{\text{I}}{2\frac{3R^2-2R^2}{6}}$

Correct!

Part $(c)v$

$If$ the total current $is9\mathrm{.}5A,$ what $is$ the value $of$ the constant $A,in$ units $of$ amperes per square meter?

$A=6\mathrm{.}63**{10}^7$

$A=6\mathrm{.}630{10}^7\frac{A}{m^2}$

Correct!

Part $(d)$

Find $an$ expression for the magnetic field inside the wire, $r,in$ terms $of$ the current I.

$B(r)=$

${}_{0}2(\frac{\text{I}}{2\frac{3R^2-2R^2}{6}})\frac{\frac{3r^{2}R-2r^3}{6R}}{2r}$

Correct!

Part $(e)$

Find $an$ expression for the magnetic field outside $of$ the wire. That $is,$ for $r>R.$

$B(r)={}_0\frac{\text{I}}{2r},$ Correct!

Part $(f)$

For what $r,in$ 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 $ofr,in$ meters, $is$ the magnetic field maximized?

Part $(i)$

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

I ONLY NEED PART F$,$G$,$H and I please