Four identical bar magnets are placed flat on a table so that their centers occupy…
MATHEMATICS · Multi-part · A Level · Mathematics · Forces and Newton's laws · Forces and Newton's laws
Problem
Four identical bar magnets are placed flat on a table so that their centers occupy the corners of a square of side length L. Each magnet is oriented with its North pole pointing directly toward the geometric center of the square. A fifth, much smaller bar magnet P (whose length is negligible compared with L) is placed at the exact center of the square. Magnet P is oriented so that its North pole points along the positive x-axis.
Treat each pole of every magnet as a point magnetic charge of magnitude p, and use the inverse-square force law F=kp2/r2 for interactions between any two poles separated by distance r. The thickness of the magnets is negligible, so all pole charges lie in the same horizontal plane.
(a) Determine the magnitude and direction of the net magnetic force exerted on magnet P by the four surrounding magnets. Explicitly state any symmetry arguments you use.
(b) Suppose magnet P is now rotated so that its North pole points toward one of the surrounding North poles. Without performing a full calculation, use qualitative reasoning to state whether the magnitude of the net force on P increases, decreases, or remains zero. Justify your answer.