Two long, straight wires are positioned along the x - and y -axes, respectively, with each carrying a current of 5 A . The currents are directed along the positive directions of the axes. Determine the magnetic field at the point (1 m , -1 m ) .

Step-by-step solution

The magnetic field due to a long straight wire carrying current I at a perpendicular distance r is given by B = ₀ I 2 r . For the wire along the x -axis, the current I₁ = 5 A flows in the + i direction. The point (1 m , -1 m ) is at a perpendicular distance r₁ = 1 m from the x -axis. Using the right-hand rule, the magnetic field B ₁ at this point is directed into the plane (negative z -axis). B ₁ = ₀ I₁ 2 r₁ (- k ) = 4 10⁻⁷ 5 2 1 (- k ) = -1 T k For the wire along the y -axis, the current I₂ = 5 A flows in the + j