Final answer:
To determine the magnitude of the magnetic field at point P in a system of parallel wires carrying different currents, we can use the formula for the magnetic field produced by a long straight wire. By calculating the magnetic fields produced by each wire and summing them up, we can find the total magnetic field at point P.
Step-by-step explanation:
To determine the magnitude of the magnetic field at point P, we can use the formula for the magnetic field produced by a long straight wire, which is given by:
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 in the wire, and r is the distance from the wire to the point where we want to find the magnetic field. In this case, we have three wires with different currents and distances from point P. We can find the magnetic fields produced by each wire and then sum them up to find the total magnetic field at point P.
Let's start by calculating the magnetic field produced by wire 1:
B₁ = (4π × 10⁻⁷ T·m/A ×18 A) / (2 ×π ×0.05 m) = 1.44 × 10⁻⁵ T
Similarly, we can calculate the magnetic field produced by wire 2 and wire 3:
B₂ = (4π × 10⁻⁷ T·m/A ×18 A) / (2 ×π ×0.1 m) = 9.0 × 10⁻⁶ T
B₃ = (4π × 10⁻⁷ T·m/A ×6 A) / (2 ×π × 0.1 m) = 3.0 × 10⁻⁶ T
Finally, we can sum up the magnetic fields to find the total magnetic field at point P:
B_total = B₁ + B₂ + B₃ = 1.44 × 10⁻⁵ T + 9.0 × 10⁻⁶ T + 3.0 × 10⁻⁶ T = 2.34 × 10⁻⁵ T
Therefore, the magnitude of the magnetic field at point P is approximately 2.34 × 10⁻⁵ T.