$($A$)$ The current density across a cylindrical conductor of radius R varies according to the equation j$=$ jo $(1-$ r R$),$ where r is the distance from the axis. Thus the current density is a maximum joat the axis r $=0$ and decreases linearly to zero at the surface ~ $=$ R$.$ Calculate the total current Ithrough the wire in terms of jo and the conductor's cross$-$sectional area A $=$ R$?.$ Hint: Dividethe cross$-$section of the wire into little donuts $($annuli$)$ of inner radius r and outer radius r $+$ dr$.$Then use an integral to add up all the pieces of current dI $($r$)$ contained in each annulus.!$($B$)$ Suppose that, instead, the current density is a maximum jo at the surface and decreases linearly to zero at the axis, so that j$=$ jor$/$R$.$ Now calculate the current. Why is the current larger $($you should find it's twice as large$)$ than in part $($A$)?$