Two parallel wires are separated by a distance of 2.0 cm and carry equal currents of 10 A in the same direction. Determine the magnitude of the magnetic field at a point located 2.0 cm away from each of the two wires.

Step-by-step solution

Let the two wires be at points A and B, and the observation point be P. Since the distance between the wires is 2.0 cm and point P is 2.0 cm away from both wires, triangle PAB is an equilateral triangle with side length a = 2.0 cm = 0.02 m . The magnitude of the magnetic field at P due to each wire is: B₁ = B₂ = ₀ I 2 a Substituting the given values: B₁ = 4 10⁻⁷ 10 2 0.02 = 10⁻⁴ T The magnetic field vectors B ₁ and B ₂ are perpendicular to the position vectors connecting the wires to point P. Since the angle betwee