Physics
Physics
Problem
A semicircular wire of radius lies flat on a table. Two straight leads connect the ends of the semicircle directly to its center, forming a closed path. A constant current leaves the center along one radial lead, travels around the semicircle in the clockwise direction as seen from above, and returns along the other radial lead. Neglect any magnetic field produced by the radial leads at the center. Which statement best describes the direction of the magnetic field at the center due only to the current in the semicircular portion? a) b) c) d)Intuitive explanation
The key is to use the Biot-Savart law (or the right-hand rule) to find how each tiny segment of the curved wire contributes to the field at the center. Every element of the semicircle is at the same distance from the center, and when you curl your fingers in the direction of current flow around the semicircle, your thumb points perpendicular to the plane—either up or down depending on which way the current curves. Since all segments curve the same way, their contributions add constructively in one direction rather than canceling.
Intuitive explanation
The key is to use the Biot-Savart law (or the right-hand rule) to find how each tiny segment of the curved wire contributes to the field at the center. Every element of the semicircle is at the same distance from the center, and when you curl your fingers in the direction of current flow around the semicircle, your thumb points perpendicular to the plane—either up or down depending on which way the current curves. Since all segments curve the same way, their contributions add constructively in one direction rather than canceling.