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Suppose that instead the current density...

Suppose that instead the current density is a maximum `J_(0)` at the surface and decreases linearly to zero at the axis so that `J=J_(0)(r )/(R )`. Calculate the current.

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To solve the problem, we will calculate the total current flowing through a cylindrical conductor where the current density \( J \) varies with the radius \( r \). The current density is given by: \[ J = J_0 \frac{r}{R} \] where \( J_0 \) is the maximum current density at the surface (at \( r = R \)) and decreases linearly to zero at the center (at \( r = 0 \)). ...
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