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## Homework Statement

Suppose a wire has a radius [itex] R[/itex] and a current density of [itex]J = I_0 \frac{x^2} {R^4}\hat{k}[/itex]. Taking the wire to have cylindrical geometry, calculate the total current flowing down the wire, defined as [itex]I = \int J \cdot \vec{dA} [/itex].

## Homework Equations

[itex]J = I_0 \frac{x^2} {R^4}\hat{k}[/itex]

[itex]I = \int J \cdot \vec{dA} [/itex]

## The Attempt at a Solution

Here, I assumed that dA = R dR dx . I then attempted to do the Integral. I assumed I

_{o}was a constant, so I pulled that out of the Integral, giving me...

[itex]I = I_o\int x^2\cdot \vec{dx} \int R^{-3} \cdot \vec{dR} [/itex]

Evaluating, I got...

[itex]I = I_o\frac{x^3}{3}\frac{R^{-2}}{-2}\hat{k}[/itex]

I have no idea if this is right or wrong. I don't even know if I'm on the right track. Please, any sort of help you could give me would be greatly appreciated!