Two capacitors have the same plate separation, but one has square plates and the

Question

Two capacitors have the same plate separation, but one has square plates and the other has circular plates. The square plates are a length L on each side, and the diameter of the circular plate is L. The capacitors have the same capacitance because they contain different dielectric materials. The dielectric constant of the material between the square plates has a value of ?square = 2.57. What is the dielectric constant ?circular of the material between the circular plates?

Explanation / Answer

Capacitance of a parallel plate capacitor is: C = e_r · e0 · A/d (e_r dielectric constant of the material bewteen the plates, e0 vacuum permittivity, A plate area, d distance between the plates) Thus, C_circle = C_square e_circle · e0 · A_circle/d = e_square · e0 · A_square/d e_circle · e0 · (p/4)·L²/d = e_square · e0 · L²/d => e_circle = (4/p)·e_square = (4/p)·2.57 = 3.67

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