As shown in the figure, a long wire is bent at its middle to form a right angle. The magnitudes of the magnetic fields at the points P , Q , R , and S are equal. Determine this common magnitude.

Step-by-step solution

Let the bend of the wire be at the origin (0,0) . The wire consists of two semi-infinite segments: 1. A vertical segment along the negative y-axis. 2. A horizontal segment along the negative x-axis. The given points are P(0, -d) , Q(d, 0) , R(0, d) , and S(-d, 0) . Consider the magnetic field at point P(0, -d) : Point P lies on the vertical segment, so the magnetic field due to this segment at P is zero. Point P is at a perpendicular distance d from the end of the semi-infinite horizontal segment. The magnetic fiel