~E(z_0) = \left\{ \begin{array}{ll} \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 \end{array} \right.

~E(z_0) = \left\{ \begin{array}{ll} \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 \end{array} \right.

V(z) = \left\{ \begin{array}{ll} 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 \end{array} \right.