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Spherical and Cylindrical Capacitors Gautam Chebrolu Ryan Dickmann Spherical How it looks: An inner sphere(solid) of a radius of R1 and a radius of R2 to the outer shell. Spherical(Calculations) First find the Electric Field outside the sphere: ◦ Make a spherical Gaussian surface around it ◦ The change in Electric Potential, or Voltage, is equal to the integral of the Electric Field from inner to outer radius Spherical(Calculations) Since charge on each plate is equal to the product of Capacitance and Electric Potential, reordering the equation gives: Plugging in the found Voltage the charge symbols cancel and give: Cylindrical How it looks: An inner cylinder(solid) of a radius of R1 and a radius of R2 to the outer shell. It is similar to the spherical capacitor. Cylindrical(Calculations First find the Electric Field around the cylinder using Gauss’ Law: Where lambda is the linear charge density The Voltage is equal to the integral of the Electric Field from inner to outer radius Cylindrical(Calculations) Since charge on each plate is equal to the product of Capacitance and Electric Potential, reordering the equation gives: Plugging in the found Voltage the charge symbols cancel and give: Which is Capacitance per Unit Length