Final answer:
The magnitude of the magnetic field halfway between two parallel wires carrying current in opposite directions is 10^-6 T.
Step-by-step explanation:
The magnitude of the magnetic field halfway between two parallel wires carrying current in opposite directions can be calculated using Ampere's law.
First, we need to calculate the magnetic field produced by each wire at the midpoint. The magnetic field produced by a wire carrying current I at a distance r from the wire is given by the equation B = μ₀I/2πr, where μ₀ is the permeability of free space (4π × 10^-7 T·m/A) and r is the separation between the wire and the point of interest. In this case, the separation is half the distance between the wires, so r = 2.0 m.
Since the currents are in opposite directions, the magnetic fields produced by the two wires will be in opposite directions as well. The magnitude of the magnetic field at the midpoint is the sum of the magnitudes of the magnetic fields produced by each wire. Therefore, the magnitude of the magnetic field halfway between the wires is given by:
B = μ₀I/2πr + μ₀I/2πr = (2μ₀I)/2πr
Substituting the given values into the equation, we have:
B = (2 × 4π × 10^-7 T·m/A × 10 A)/(2π × 4.0 m) = 10^-6 T