The current density in a medium is given by $${\overrightarrow J= \frac{400 \sin\theta}{2\pi(r^2+4)} \hat {a}_r \: Am^{-2}}$$

The total current and the average current density flowing through the portion of a spherical surface $r = 0.8 \: m$, $\frac{\pi}{12} \leq \theta \leq \frac{\pi}{4}$, $0 \leq \phi \leq 2\pi$ are given, respectively, by