1A current is flowing through a cylindrical conductorof radius R such

1.	1A current is flowing through a cylindrical conductorof radius R such that current density at radialdistance r is given by J =Jnote Calculatetotal current through cross-section of conductor.
Answer» you mean, current density at radial distance r is given by, $J_0\left(1-\frac{r}{R}\right)$ , right? we KNOW, current density is the rate of flowing of current through UNIT CROSS sectional area. i.e., J = dI/dA or, $I=\int{J}\,dA$ so, first of all, finding ELEMENTARY area of cylinderical conductor. A = πr² differentiating both SIDES, dA = 2πr . dr then, current, I = $\int\limits^R_0{J}\,(2\pi r).dr$ = $2\pi J_0\int\limits^R_0{\left(r-\frac{r^2}{R}\right)}\,dr$ = $2\pi J_0\left[\frac{r^2}{2}-\frac{r^3}{3R}\right]^R_0$ = $2\pi J_0\left[\frac{R^2}{2}-\frac{R^2}{3}\right]$ = $\frac{\pi J_0R^2}{3}$ This is our required answer.