# Current density

**Electricity and Magnetism**Level 3

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