# Topic Category: Laplace Equation in Spherical Polar Coordinates

## Conducting Sphere in External Electric Field

Consider a conducting sphere in a uniform electric field The bound charges appears on the surface of conducting sphere. The field produced by these bound charges exactly cancels out field inside the sphere and distorts the field outside the sphere. As bound charge has cylindrical symmetry, the electric field and potential will also have cylindrical …

## Dielectric Sphere in External Electric Field

Example 7 : A dielectric sphere of radius a and dielectric constant is placed in a dielectric liquid of infinite extent and dielectric constant . A uniform electric field E was originally present in the liquid. Find the resultant electric field inside and outside the dielectric sphere. Solution : Before putting dielectric sphere, electric field …

## Laplace Equation in Spherical Polar Coordinates

In spherical polar coordinates, Laplace equation can be written as Using separation of variables Substituting it in Laplace equation and dividing the whole equation by LHS is function of r and while RHS is function of only. Thus, both sides must be equal to the same constant say . Then, So, The other equation is …