The current density across a cylindrical conductor of radius R varies in magnitude according to the equation `J = J_0(1 - (r )/(R ))` where r is the distance from the central axis. Thus, the current density is a maximum `J_0` at that axis (r = 0) and decreases linearly to zero at the surface (r = R). Calculate the current in terms of `J_0` and the conductor 's cross - sectional area `A = piR^2`.

Explanation

To calculate the current flowing through a cylindrical conductor with a varying current density, we can follow these steps:

### Step 1: Understand the Current Density Equation
The current density \( J \) is given by the equation:
\[ J = J_0 \left(1 - \frac{r}{R}\right) \]
where:
...