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 solve the problem of finding the current in a cylindrical conductor where the current density varies with distance from the axis, we can follow these steps:

### Step 1: Understand the current density equation
The current density \( J \) is given by:
\[ J = J_0 \left(1 - \frac{r}{R}\right) \]
where \( J_0 \) is the maximum current density at the center (when \( r = 0 \)) and it decreases to zero at the surface of the conductor (when \( r = R \)).
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