Given, current density, J=β(r+r0)2=β(r2+2rr0+r02) We know that, current density, J=‌
‌ Current ‌(I)
Area(A)
⇒ Current, I=J⋅A or dI=J⋅dA ‌⇒‌‌∫dI=∫J⋅dA ‌⇒‌‌I=∫β(r2+2πr0+r02)⋅dA Where, dA is area element in cartesian coordinate. In polar coordinates dA=rdrdθ ∴‌‌I=2β‌
π∕6
∫
0
dθ‌
R
∫
0
(r2+2r0+r02)rdr ( ∵ for θ,0 to π‌backslash‌6 and 5π‌backslash‌6 to π is symmetric) ‌=2β[θ]0π∕6[