A long, straight wire conducts a current along the z -axis. It is possible to identify two distinct points in the x – y plane such that

Step-by-step solution

The magnetic field due to a long straight wire carrying current I along the z -axis at a point (x, y) in the x - y plane is given by B = ₀ I 2 (x^2 + y^2) (-y i + x j ) . The magnitude of the magnetic field is B = ₀ I 2 r , where r = x^2 + y^2 , and its direction is tangential to the circle of radius r centered at the origin. For two distinct points to have the same direction of magnetic field, they must lie on the same radial line originating from the origin. For example, points (x, y) and (2x, 2y) have the same d