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 d is given by B = ₀ I 2 d . For the wire along the x -axis, the current is in the + i direction. The position vector of the point (-1, -1) with respect to the origin on the x -axis is in the - j direction (since y = -1 m ). The magnetic field B ₁ due to this wire is: B ₁ = ₀ I 2 d ( i - j ) = 4 10⁻⁷ 5 2 1 (- k ) = -10⁻⁶ k T = -1 T k For the wire along the y -axis, the current is in the + j direction. The position vector of