Solution
= Solution
The relation $B_i=-J$ means $k_-p_i=k_+s_ic_i+J$. Put $K=k_-/k_+$ and substitute the preceding expression for $c_i$:
$$
\boxed{p_i=\frac{s_ic_e}{K}+J\left(\frac1{k_-}+\frac{s_i}{Kk}\right).}
$$
The first term is the <equilibrium> binding contribution from the outward free-carrier pool; the additional terms account for the maintained current and the excess inward-facing free carriers. This is a steady throughput relation, not a detailed-balance assumption.