# Formula for curved capacitance 'plates'

What is the capacitance formula between two (2) evenly curved plates?

Imagine these plate halves curved around on opposite ends of a cylindrical dielectric material. Assume the curvature angle as 'theta' where 0 <= theta <=180 degrees. @theta=180 degrees, they become standard parallel plate capacitors whose formula is well known.

• You mean like a Leyden Jar? Seem like a homework question to me. – Oldfart Jan 18 '18 at 19:16
• Curvature angle?!? I think you need to add a diagram that explains the geometry you're talking about. – Dave Tweed Jan 18 '18 at 19:46
• What about the capacitance between concentric spheres. Would that help because it is solved and might provide insight. – Andy aka Jan 18 '18 at 19:49
• @Oldfart ...this is NOT a homework issue but a design problem I'm working on for a customer. – David M Jan 18 '18 at 20:33
• If the diagram is at all to scale, the capacitance will be dominated by the flat areas on each side. – MikeP Jan 18 '18 at 21:12

Oh, the formula is easy: it's $$C = Q/V$$ and you find V by solving for the E field with a test charge +Q on one plate, -Q on the other, and integrating (line integral) $$V = \int \overline E \cdot d\overline L$$ from any convenient point on one electrode, to the other.