Two hollowed metallic spheres centered at the same point form a spherical capacitor. The space between the two spheres is filled with a dielectric material. R₁ - R₂ = 1.5 mm, where R₁ and R ₂ are radii of the outer and inner spheres, respectively. The capacitor has a capacitance of 0.500 nF. Find values of R₁ and R₂.

A BNC-to-BNC cable used to transmit signals to a cathode ray oscilloscope has a coaxial cable between the connectors. The central copper wire has a diameter of 0.94 mm, while the 0 V silver-plated copper double braid surrounding the central copper conductor has a diameter of 3.53 mm. A dielectric material separates the two conductors. A jacket is used to insulate the entire assembly. Calculate capacitance per meter (C/m) for the BNC cable.

Even though spherical capacitors are very practical, we can still predict their capacitance theoretically. Derive an expression for the capacitance of the assembly of two hollowed conducting balls of diameter d₁ (outer ball) and d₂ (inner ball) that form a spherical capacitor.

A high-precision measurement device uses a long cylindrical capacitor consisting of four concentric metallic cylinders with radii 𝑅₁, 𝑅₂, 𝑅₃, and 𝑅₄. In this setup, all cylinders are made of copper. The cylinders Copper strips connect 2 and 3 to ensure they are at the same potential. Calculate the capacitance per unit length of this arrangement, assuming equal and opposite charges are placed on the innermost cylinder 𝑅₁ and the outermost cylinder 𝑅₄. The capacitance of the cylindrical capacitor is $C=\frac{2\pi \epsilon _0\ell }{\ln \left(\frac{R_{outer}}{R_{inner}}\right)}$.