Physics
Physics
Problem
Three long, straight wires form the vertices of an equilateral triangle of side 0.12 m that lies in a horizontal plane. Each wire carries a current of 6.0 A directed into the page. The centroid C of the triangle is 0.069 m from each vertex. (a) Determine the magnitude of the magnetic field at the centroid C produced by a single wire. (b) Calculate the magnitude and direction of the net magnetic field at the centroid due to all three wires. Explain your vector addition clearly. (c) The current in one of the wires is increased to 12 A while the other two remain at 6.0 A into the page. Determine the new magnitude of the net magnetic field at the centroid and describe its direction relative to the plane of the triangle.Intuitive explanation
The key insight is that magnetic field superposition lets you add the individual fields from each wire as vectors. Since all three currents point the same direction (into the page), each wire creates a field that circles around it by the right-hand rule—and by symmetry, these three fields meet at the centroid with equal magnitude but different directions. You'll use for each wire, then add them vectorially, exploiting the 120° rotational symmetry to find the net field.
Intuitive explanation
The key insight is that magnetic field superposition lets you add the individual fields from each wire as vectors. Since all three currents point the same direction (into the page), each wire creates a field that circles around it by the right-hand rule—and by symmetry, these three fields meet at the centroid with equal magnitude but different directions. You'll use for each wire, then add them vectorially, exploiting the 120° rotational symmetry to find the net field.