Two long straight parallel wires are separated by a distance d . They carry currents I and nI in opposite directions. Point M is located exactly midway between the two wires. Point P is located outside the region between the wires, at a distance d from the wire carrying current nI and 2d from the wire carrying current I . If the ratio of the magnitude of the magnetic field at M to that at P is 4 , find the value of t

Step-by-step solution

Let the wires be wire 1 (carrying current I ) and wire 2 (carrying current nI ). At point M , which is midway between the wires, the distance from each wire is d/2 . Since the currents are in opposite directions, the magnetic fields due to both wires at M point in the same direction and add up. B_M = ₀ I 2 (d/2) + ₀ (nI) 2 (d/2) = ₀ I d (1 + n) At point P , the distance from wire 2 is d and from wire 1 is 2d . The magnetic fields due to the two wires will be in opposite directions. B_P = | ₀ (nI) 2 d - ₀ I 2 (2d) |