Conservation laws, electromagnetic waves, radiation, relativistic formulation of electrodynamics and potential fields.
Deepen their understanding of electromagnetism, junior-level E&M, and necessary math skills. See the various topics in the course as part of a coherent theory of electromagnetism; i.e., as a consequence of Maxwell’s equations. Translate a description of an E&M problem into the mathematical equation(s) necessary to solve it; explain the physical meaning of the solution, including how this is reflected in its mathematical formulation; and be able to achieve physical insight through mathematics. Articulate the important ideas from each chapter and section, thus indicating how they have organized their content knowledge. They should be able to filter this knowledge to access the information they will need to solve a particular physics problem. Justify and explain their thinking and/or approach to a problem or analysis of a physical situation, in either written or oral form. Students should be able to understand and summarize a significant portion of an appropriately difficult scientific paper on a topic covered in this course. Choose and apply the problem-solving technique that is appropriate for a particular situation. They should be able to apply these methods to novel contexts (i.e., solving problems that do not come from a textbook), indicating how they understand the essential features of the technique, rather than just the rote mechanics of its application. Effectively use approximation techniques, and recognize when they are appropriate. They should be able to decide how many terms of a series expansion must be retained to find a solution of a given order, and be able to complete a Taylor Series to at least two terms. Recognize symmetries, and be able to take advantage of them when choosing the appropriate method of solution. Write down the line, surface or volume integral required for solving a specific problem, and correctly follow through with the integration. Recognize that a general solution can be formed by the superposition of multiple components, and a specific solution found by applying appropriate boundary conditions. Draw on an organized set of content knowledge, and apply problem-solving techniques with that knowledge in order to carry out lengthy analyses of physical situations. They should be able to connect all the pieces of a problem to reach a final solution. Students should be able to articulate what it is that needs to be solved for in a given problem, and know when they have found it. Articulate their expectations for the solution. For all problems, students should be able to justify the reasonableness of a solution (e.g., by checking its symmetry, looking at limiting or special cases, relating to cases with known solutions, dimensional analysis, and/or checking the scale/order of magnitude of the answer). Recognize the utility and role of formal derivations and proofs in the learning, understanding, and application of physics. They should be able to identify the necessary elements of a formal derivation or proof; and be able to reproduce important ones, including an articulation of their logical progression. They should have some facility in recognizing the range/limitations of a result based on the assumptions made in its derivation.