Four point charges are fixed at the corners of a square of side length that lies in…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Four point charges are fixed at the corners of a square of side length a that lies in the xy–plane. Starting at the upper left corner and moving clockwise, the charges are +q, +q, −q, and +q. A small positive test charge Q is placed at the center of the square and released from rest.
(a) Determine the direction of the initial acceleration of the test charge. Provide a step-by-step qualitative argument based on the individual forces exerted by the four corner charges.
(b) Rank the magnitudes of the four individual forces exerted on the test charge by the corner charges. Justify your ranking without performing explicit numerical calculations.
(c) The charge at the lower right corner is now moved to the midpoint of the right side of the square while its magnitude remains −q. Predict qualitatively whether the magnitude of the net force on the test charge increases, decreases, or remains the same compared to part (a). Explain your reasoning.
(d) Restore the negative charge to its original corner position but change its magnitude to −2q. Describe how (i) the direction and (ii) the magnitude of the net force on the test charge compare with those found in part (a). Support each comparison with qualitative reasoning.