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Given the vector current density, determine the total current flowing outward through a circular band

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Given the vector current density, determine the total current flowing outward through a circular band.:

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The answer should be 518A. It comes something around 3255 A. Where is the mistake?

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asked Mar 29 in Physics Problems by Anwesa Roy (120 points)
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.

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