Alternating current flowing through a conductor prefers to flow close to the surface so the current density in the conductor increases with radial position. If we assume the current is of the form, \(I=q_{e}^{\prime \prime}(r) \exp (i \omega t)\), the differential equation describing the current density, \(q_{e}^{\prime \prime}\), becomes:

\[\frac{d^{2} q_{e}^{\prime \prime}}{d r^{2}}+\frac{1}{r} \frac{d q_{e}^{\prime \prime}}{d r}-i\left(\frac{4 \pi \omega^{2}}{ho}\right) q_{e}^{\prime \prime}=0\]

where \(ho\) is the resistivity of the conductor. Determine the current density as a function of radial position for a cylindrical conductor of radius, \(r_{o}\), when the current density at the surface is \(q_{e o}^{\prime \prime}\).