PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism
Problem
Four infinitely long, straight conductors are positioned at the corners of a square of side length a that lies in the plane z = 0. The square’s sides are parallel to the x- and y-axes, and its center is at the origin. Each conductor carries a current of identical magnitude I, but the directions are as follows:
• Top-left corner: current directed out of the page (toward +z).
• Top-right corner: current directed out of the page.
• Bottom-left corner: current directed into the page (toward −z).
• Bottom-right corner: current directed into the page.
A very short, straight wire segment of length L is placed along the square’s diagonal from the bottom-left corner toward the top-right corner, centered at the origin. The current in this segment is directed from the bottom-left toward the top-right.
(1) Determine the direction of the net magnetic field at the center of the square that results from the four corner conductors. Provide a qualitative explanation based on superposition.
(2) Without computing numerical values, compare the contributions of each conductor to the magnitude of the field at the center. Identify which conductors contribute equally and whether any conductor’s contribution is larger or smaller than the others. Justify your reasoning.
(3) State the direction of the net magnetic force acting on the short wire segment along the diagonal. Explain clearly how you arrive at this direction, considering the spatial variation of the magnetic field along the segment.
(4) Discuss qualitatively whether the segment experiences a net torque about the center of the square. Support your answer with physical reasoning.