Originally Posted by

**jezzyjez** Hey I have been given the below question but am really struggling to get even the first part:

We want to find the value of the electrostatic potential $\displaystyle \phi(r,\theta)$ in the quadrant.

$\displaystyle 0 \leq r \leq b$ , $\displaystyle 0 \leq \theta \leq \frac{\pi}{2}$

where $\displaystyle r$ and $\displaystyle \theta$ are the standard polar co-ordinates and $\displaystyle b$ is a given positive real number. Assuming electrostatic potential is the solution of Laplaces equation in polar co-ordinates

$\displaystyle \frac{\delta^2 \phi}{\delta r^2} +\frac{1}{r}\frac{\delta\phi}{\delta r} + \frac{1}{r^2} \frac{\delta^2\phi}{\delta\theta^2} = 0$

The boundary conditions on $\displaystyle \phi(r,\theta)$ are

$\displaystyle \phi(b,\theta) = \frac{4}{\pi^2} \theta(\pi - \theta),$

$\displaystyle \phi(r,0) = 0, \phi(r,\frac{\pi}{2}) = 1$

(a) State why the differential equation with the given boundary conditions can't be solved by the method of separating variables.

The problem I am having is that I can separate the equation into to parts so I am assuming it is to do with the boundary conditions why it cannot be solved, but I don't know what aspect of the conditions effects this?