(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the electric potential inside and outside a spherical capacitor, consisting of two hemispheres

of radius 1 m. joined along the equator by a thin insulating strip, if the upper hemisphere is kept

at 220 V and the lower hemisphere is grounded

2. Relevant equations

u (r,θ) = ρ(r)y(θ)

Laplacian in spherical parts: -Δ^2 = [itex]\frac{1}{sin(θ)}[/itex] [itex]\frac{∂}{∂θ}[/itex](sinθ [itex]\frac{∂}{∂θ}[/itex]) + [itex]\frac{1}{sin^2(θ)}[/itex][itex]\frac{∂^2}{d\phi^2}[/itex]

where we can assume that this does not depend on [itex]\phi[/itex] because rotation is symmetric

3. The attempt at a solution

Two equations:

[itex]\frac{1}{r^2}[/itex][itex]\frac{∂}{∂r}[/itex] (r^2 ρ'(r)) + λy=0

[itex]\frac{1}{sin(θ)}[/itex][itex]\frac{∂}{∂θ}[/itex] (sin(θ)[itex]\frac{∂y}{∂θ}[/itex]) - λy=0

I believe that I am supposed to somehow convert this into Legendre's equation, but I'm not sure how to do this.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Electric potential inside and outside spherical capacitator using laplacian

**Physics Forums | Science Articles, Homework Help, Discussion**