Current density

The current density across a cylindrical conductor with radius A A varies according to the following relation: J = K ( 1 x A ) , \overrightarrow { J } = \overrightarrow { K } \left(1 - \frac{x}{A}\right), where K \overrightarrow { K } is the constant vector across the length of the conductor and x x is the distance from the axis of the cylinder. Find the current through the cylindrical cross-section.

K π A 2 6 \frac{\overrightarrow { K } \pi A^2}{6} K A 2 2 \frac{\overrightarrow { K } A^2}{2} K A 2 3 \frac{\overrightarrow { K } A^2}{3} K π A 2 3 \frac{\overrightarrow { K } \pi A^2}{3}

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