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Problem 1 A vector field is given in cylindrical coordinates as ๐นโƒ— = ๐ด ๐ด ๐œ‘๏ฟฝ + ๐ต ๐ต ๐ต ฬ‚ where A and B are constants. Could ๐นโƒ—be an electrostatic field? Why or why not? Problem 2 i) Two point charges, 3q and โ€“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 ๐œŽ = ๐œŽ0 cos 2๐œƒ 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?

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Electricity and Magnetism Problems
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