Capacitance Using Calculus Practice Problems

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 central brass ball and a concentric brass shell form a spherical capacitor. The central brass ball has a radius R₁ and the shell has an inner radius of 5.10 cm. If a voltage of 180 V is applied across the plates, the central ball and the shell are charged with 5.00 nC and -5.00 nC, respectively. What are i) the capacitance (C) of the device, ii) the numerical value of R₁, and iii) the electric field (E) at the surface of the central ball?

A cylinder-shaped capacitor consists of a copper cylinder of radius 3.00 cm surrounded concentrically by a copper cylindrical shell of inner radius 4.00 cm. Both the cylinder and the shell have the same length of 10.00 cm. The cylinder is negatively charged with a charge of 50 pC, while the shell is positively charged with a charge of - 50 pC. Find the i) capacitance (C) of this cylindrical capacitor and ii) the potential difference (ΔV) required across this capacitor to generate these charges.

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.