Question

suppose that the current density through a cross section varies with radial distance r as j = ar2 in which a = 3.0*10^11A/m4 and r is in meters. what is the current through the outer portion of the wire?

Answer 1

$I=\displaystyle{\int^R_0}2\pi rjdr=\displaystyle{\int^R_0}2\pi r\cdot ar^2dr=(2\pi a r^4/4)|^R_0=2\pi a R^4/4$

where R is radius of wire.