Final answer:
a) The magnetic field created by I at point A is 5.0 × 10^-5 T. b) The magnetic field created by I₂ at point A is 4.6 × 10^-5 T. c) The net magnetic field at point A is 9.6 × 10^-5 T. d) The direction of the net magnetic field is opposite to the magnetic field created by I.
Step-by-step explanation:
a) To calculate the magnetic field created by I at point A, we can use the formula for the magnetic field created by a straight wire:
B = (μ₀ * I) / (2 * π * r)
where B is the magnetic field, μ₀ is the permeability of free space (4π × 10^-7 T·m/A), I is the current, and r is the distance from the wire. Since point A is the midpoint between the wires, the distance from each wire to point A is d/2 = 5.0 cm. Plugging in the values, we get:
B₁ = (4π × 10^-7 T·m/A * 12.5 A) / (2 * π * 0.05 m) = 5.0 × 10^-5 T
b) To calculate the magnetic field created by I₂ at point A, we can use the same formula:
B₂ = (μ₀ * I₂) / (2 * π * r)
Using the same distance of 5.0 cm, we get:
B₂ = (4π × 10^-7 T·m/A * 11.6 A) / (2 * π * 0.05 m) = 4.6 × 10^-5 T
c) The net magnetic field at point A is the vector sum of the magnetic fields created by I and I₂:
B_net = B₁ + B₂ = 5.0 × 10^-5 T + 4.6 × 10^-5 T = 9.6 × 10^-5 T
d) The direction of the net magnetic field depends on the direction of the individual magnetic fields created by I and I₂. Since the currents in the wires are in opposite directions, the magnetic fields created by each wire have opposite directions. Therefore, the net magnetic field at point A would have a direction opposite to the magnetic field created by I.