Four long, straight wires, each carrying a current of 5.0 A , are arranged in a plane. Their points of intersection create a square with a side length of 5.0 cm , with centre P . Points Q₁ , Q₂ , Q₃ , and Q₄ are located on the diagonals of this square at a distance from P equal to the length of the square's diagonal, as shown in the figure. Determine the magnetic fields at these four points.

Step-by-step solution

Let the centre of the square be the origin (0,0) . The side length of the square is a = 5.0 cm = 0.05 m . The four wires are located at x = -a/2 , x = a/2 , y = -a/2 , and y = a/2 . The currents are I = 5.0 A in the +y direction for the vertical wires and in the +x direction for the horizontal wires. The diagonal of the square is d = a 2 . The points Q₁, Q₂, Q₃, Q₄ are at a distance d from the origin along the diagonals. Their coordinates are: Q₁ = (-a, a) Q₂ = (a, a) Q₃ = (a, -a) Q₄ = (-a, -a) The magnetic field d