Capacitors & Capacitance Practice Problems

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.