Question

One long wire carries a current of 30A along the entire x axis. A second long wire carries a current of 40A perpendicular to the xy plane and passing through a point (0, 4, 0)m. What is the magnitude of the resulting magnetic field at the point y-2.0m on the y-axis?

Answer 1

Two wires: One wire is carrying the current I_1 in the positive x-direction (suppose) and second wire carries current I_2 placed at point (0, 4, 0). suppose the current I_2 is following into the page. The resulting magnetic field at point A(y = 2.0 m) can be determined using the superposition principle. B vector = B_1 vector + B_2 vector ---(1) B_1 vector: Using Ampere's law: integral B_1 vector middot dl vector = mu_0 I_1 B_1 = mu_0 I_1/2 pi r r = 2.0 m B_1 vector = mu_0 I_1/2 pi (2) z hat = 30 mu_0/4 pi z hat B_1 vector = 30/4 pi mu_0 z hat \r\n B_2 vector: Using Ampere's law: integral B_2 vector middot dl vector = mu_0 I_2 B_2 = mu_0 I_2/2 pi r = mu_0 (40)/2 pi (2) = 40/4 pi mu_0 B_2 vector = 40/4 pi mu_0 (-x hat) from (1) B vector = 30/4 pi mu_0 z hat + 40/4 pi mu_0 middot (-x hat)