On a square wireframe with side length a in empty space, there is a linear charge density ρl. Calculate a · ρl numerically by finding a solution for the values of a and ρl required for the potential at the center of this square frame to be V = 2 ke [Volts].

An air-gap parallel-plate capacitor that has a plate area of 1.20 m2 and a separation of 1.40 mm is charged to 90 V. (a) What is the electric field between the plates? kV/m (b) What is the electric energy density between the plates? |mJ/m3 (c) Find the total energy by multiplying your answer from Part (b) by the volume between the plates. (d) Determine the capacitance of this arrangement. nF (e) Calculate the total energy from U = V2CV2, and compare your answer with your result from Part (c).

Two 0.01 m radius spherical +1.0 µC uniform charge distributions are placed 0.2 m apart. How much electrical energy is contained in this system? It requires energy to form each of the spherical charge distributions as well as bring the two spheres together. Let us call the energy required to form the spherical charge distribution Wformation: Let us call the energy required to assemble or bring together the charges Wassembly: So, Wtotal = 2 x Wfor Formation + Wassembly The energy Wformation (in Joules) can be calculated as follows: 3 Q? Wformation 5 4πεα Where Q is the total charge of the sphere in Coulombs and a is the radius of the sphere in

Two conducting concentric spherical shells have radii a = 0.165 m and b = 0.24 m.  Part (a) Express the capacitance of the two concentric shells in terms of radii a and b and the Coulomb constant k. Part (b) Calculate the numerical value of the capacitance in F. Part (c) Express the capacitance C through the potential difference△V across the capacitor and charge Q. Part (d) If the charge in the inner sphere is +Q = 3 µC, the outer sphere -Q = -3 µC, calculate the electric potential difference△V between the outside and the inside conductors in V.