Electricity and Magnetism Problems

Problem 1 A vector field is given in cylindrical coordinates as 𝐹⃗ = 𝐴 𝐴 𝜑� + 𝐵 𝐵 𝐵 ̂ where A and B are constants. Could 𝐹⃗be an electrostatic field? Why or why not? Problem 2 i) Two point charges, 3q and –q, are separated by a distance a. For each of the arrangements in the figure below find the i) monopole moment, ii) dipole moment, and iii) the quadrupole moment. ii) For the configuration in (a) what is the potential function? Problem 3 A sphere of radius a has a surface charge distribution that is given by 𝜎 = 𝜎0 cos 2𝜃 Find the potential at all points exterior to the sphere. Describe the charge distribution in terms of multipole moments. Problem 4 Two semi-infinite grounded conducting planes meet at right angles. In the region between there is point charge q situated as shown in the figure. i) What should the image configuration be? ii) What is the potential in the region where the charge is located? iii) What is the force on q?