Physics
Physics
Problem
A U-shaped permanent magnet has a 1.5 cm wide air gap between its two poles. In a student’s sketch of its magnetic field, 30 field lines are found to pass perpendicularly through a rectangular area of located inside the gap, while only 6 field lines pass perpendicularly through an identical area situated 3 cm outside the magnet. a. (i) Draw the magnetic field pattern of the U-shaped magnet, clearly showing the regions of strongest and weakest field. b. (ii) Assuming that the magnetic field strength is directly proportional to the number of field lines per unit area, calculate the ratio of the magnetic field strength inside the gap to that outside the magnet. c. (iii) State any two practical consequences of the high magnetic field inside the gap of a U-shaped magnet.Intuitive explanation
The key insight is that magnetic field strength is proportional to the density of field lines—how many pass through a unit area. By counting field lines through the same-sized area in two different regions, you can directly compare the field strengths without needing to measure the field itself. The dramatic difference between 30 lines in the gap and 6 lines outside reveals how the field concentrates between the poles and spreads out into free space.
Intuitive explanation
The key insight is that magnetic field strength is proportional to the density of field lines—how many pass through a unit area. By counting field lines through the same-sized area in two different regions, you can directly compare the field strengths without needing to measure the field itself. The dramatic difference between 30 lines in the gap and 6 lines outside reveals how the field concentrates between the poles and spreads out into free space.