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This lecture delves into the calculation of the magnetic field at the center of a square current loop, which is more complex than a circular loop. The instructor explains the process step by step, from parametrizing the integration path based on angles to expressing the necessary elements in terms of the angle alpha. By applying geometric considerations and trigonometric functions, the lecture demonstrates how to derive the final value of the magnetic field at the center of the square loop. The detailed calculations and explanations provide a thorough understanding of the mathematical methods involved in determining the magnetic field in a non-trivial geometry.