PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Four identical point charges, each of magnitude q, are fixed at the corners of a square of side length a that lies in the xy-plane. Three of the charges are positive; the charge at the lower-right corner is negative. The square’s center is at the origin, and the corners are located at (±a/2,±a/2). Points of interest are as follows:
• Point G: the geometric center of the square (0,0).
• Point H: the midpoint of the right side of the square (a/2,0).
• Point J: the midpoint of the top side of the square (0,a/2).
A positive test charge is conceptually placed at each point to probe the field.
(a) For each of the three points (G, H, J), indicate the direction of the net electric field vector. Express each direction in terms of the coordinate axes (for example, “toward the +x direction” or “toward the –y direction”).
(b) Compare the magnitudes of the net electric fields at points G and H. State which is larger or whether they are equal, and justify your answer using vector superposition principles.
(c) Derive—without computing exact magnitudes—the relative ordering of field strengths at points G, H, and J from greatest to least. Clearly articulate how symmetry (or lack thereof) and distance considerations inform your ordering.
(d) Suppose the negative charge at the lower-right corner is replaced by a positive charge of equal magnitude. Qualitatively predict how each answer in parts (a), (b), and (c) would change, and explain the physical reasoning behind each change.