(Solved): The Poisson equation relates the electrostatic potential and charge density as shown below: \[ \na ...

The Poisson equation relates the electrostatic potential and charge density as shown below: \[ \nabla^{2} \phi=-\frac{\rho}{\varepsilon_{o} \varepsilon} \] By extending the Laplacian operator, \( \nabla^{2} \), expression in the spherically symmetrical field, derive \[ \phi=\frac{Z_{i} \in}{4 \pi \varepsilon_{o} \varepsilon a}-\frac{Z_{i} \in}{4 \pi \varepsilon_{o} \varepsilon a} \cdot \frac{1}{1+\kappa a} \]