I don't see any mistake. The difference is a factor of exactly $2\pi$, which should be in the formula.

According to the answer in part (a) the radial current density at $\rho=3, z=2$ is $180A/m^2$. The surface area of the band is $2\pi \times 3 \times 0.8$ so if the current density were constant the current through the band would be $2714A$. The current density increases with z so the total current must be greater than $2714A$. The answer of $518A$ must be wrong.

You need to have more confidence in your calculations. Also learn to make estimates and checks such as the one I did above.

According to the answer in part (a) the radial current density at $\rho=3, z=2$ is $180A/m^2$. The surface area of the band is $2\pi \times 3 \times 0.8$ so if the current density were constant the current through the band would be $2714A$. The current density increases with z so the total current must be greater than $2714A$. The answer of $518A$ must be wrong.

You need to have more confidence in your calculations. Also learn to make estimates and checks such as the one I did above.

edited Apr 15 by sammy gerbil