~E(z_0) = \left\{ \frac{\rho_0 \delta}{\epsilon_0} \left[ 1 - \exp\left(-\frac{2a}{\delta}\right) \right] \hat{z} \text{ if } z_0 > a, \; -\frac{\rho_0 \delta}{\epsilon_0} \left[ 1 - \exp\left(-\frac{2a}{\delta}\right) \right] \hat{z} \text{ if } z_0 < -a \right. \right\}

~E(z_0) = \left\{ \frac{\rho_0 \delta}{\epsilon_0} \hat{z} \text{ if } z_0 > a, \; -\frac{\rho_0 \delta}{\epsilon_0} \hat{z} \text{ if } z_0 < -a \right. \right\}

V(z) = \left\{ V_0 \text{ if } -a \leq z \leq a, \; V_0 - \frac{\rho_0 \delta}{\epsilon_0}(z - a) \text{ if } z > a, \; V_0 + \frac{\rho_0 \delta}{\epsilon_0}(z + a) \text{ if } z < -a \right. \right\}