Final answer:
The magnitude of the magnetic field at a point that is 5.0 mm from each of the wires is 0 T.
Step-by-step explanation:
To determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires, we can use the Biot-Savart law. The Biot-Savart law states that the magnetic field produced by a current-carrying wire is directly proportional to the current, inversely proportional to the distance from the wire, and depends on the direction of the current.
Applying the Biot-Savart law, we can calculate the magnetic field from each wire and then find the resultant magnetic field at the point of interest.
- The magnetic field from each wire is given by: B = (μ0 * I) / (2π * r)
- Where μ0 is the permeability of free space (4π * 10^-7 Tm/A), I is the current (20 A), and r is the distance from the wire (5.0 mm = 0.005 m).
- Using this formula, we can calculate the magnetic field from each wire and then find the magnitude of the resultant magnetic field.
Let's calculate:
- For each wire: B = (4π * 10^-7 Tm/A * 20 A) / (2π * 0.005 m) = 4 * 10^-3 T = 0.004 T
- Since the two currents are oppositely directed, the magnetic field contributions from each wire will have opposite directions.
- The resultant magnetic field can be found by subtracting the magnetic field from one wire from the magnetic field from the other wire.
So, the magnitude of the magnetic field at the point that is 5.0 mm from each of the wires is 0 T.