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.

A coaxial cable has an internal conductor with a radius of 1 mm and an external conductor with a radius of 3 mm. The voltage difference between them is set to be -500 V. What is the electric field at the surface of the internal conductor?

Consider a circuit where three capacitors (with capacitances of 5.0 μF, 7.0 μF, and 4.0 μF) have a series connection. Calculate the effective capacitance of this circuit.

While assembling an electric circuit, a student connects a network of three capacitors, C₁ = 10 pF, C₂ = 7 pF, and C₃ = 8 pF, as displayed in the figure. What is the equivalent capacitance (C_eq) between the two points, L and M?

Determine the equivalent capacitance between points M and N of the arrangement of the capacitors shown in the figure below.

(i) Calculate the potential difference between the plates of a parallel-plate air capacitor. Each plate has a charge of magnitude 0.200 μC, and the capacitance of the capacitor is 300 pF. The plates are separated by a distance of 0.400 mm.

(ii) Determine the area of each plate in the same parallel-plate capacitor described above.

(iii) Compute the magnitude of the electric field between the plates of the capacitor.

(iv) Find the surface charge density on each plate of the capacitor.

Use: $\epsilon_{0}=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}$

A pair of copper electrodes, each with a diameter of 5.0 cm, are separated by 0.80 mm. What is the magnitude of the charge on each electrode if these electrodes are connected to a 300 V power supply?

A physics student connects two identical parallel-plate capacitors with a capacitance of 4 μF to a battery with a voltage difference of 10 V, either in series or in parallel. The two plates are separated by a distance of 1mm.  Determine i) the ratio of the energy stored (U_series/U_parallel). ii) the ratio of the maximum amount of charge stored (Q_series/Q_parallel), and iii) the ratio of the electric field (E_series/E_parallel) between the two plates.