The current density across a cylindrical conductor of radius R varies according to the equation J=J0(1−rR), where r is the distance from the axis. Thus, the current density is a maximum J0 at the axis r=0 and decreases linearly to zero at the surface r=R. Calculate the current, I in terms of J0 if the conductor's cross sectional area is A=πR2.

The current density across a cylindrical conductor of radius R varies

1.	The current density across a cylindrical conductor of radius R varies according to the equation J=J0(1−rR), where r is the distance from the axis. Thus, the current density is a maximum J0 at the axis r=0 and decreases linearly to zero at the surface r=R. Calculate the current, I in terms of J0 if the conductor's cross sectional area is A=πR2.
Answer» The current density across a cylindrical conductor of radius $R$ varies according to the equation $J = J_{0} (1 - \frac{r}{R}),$ where $r$ is the distance from the axis. Thus, the current density is a maximum $J_{0}$ at the axis $r = 0$ and decreases linearly to zero at the surface $r = R$ . Calculate the current, $I$ in terms of $J_{0}$ if the conductor's cross sectional area is $A = π R^{2}$ .

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