Mathematics

Problem

In a long straight cylindrical conductor of radius

R=1.0\,\text{cm}

the current density varies with radial distance as

J(r)=J_0\left(1-\dfrac{r}{R}\right)

, where

J_0=4.0\times10^{6}\,\text{A m}^{-2}

. Determine the total current enclosed by a circular Amperian path of radius

R

coaxial with the conductor. a)

2.1\times10^{2}\,\text{A}

4.2\times10^{2}\,\text{A}

8.4\times10^{2}\,\text{A}

1.3\times10^{2}\,\text{A}