An infinitely long wire carrying a current of 2 A is bent at a right angle as shown in the Figure. What is the magnetic field magnitude in Tesla a point P, 10 cm from the corner?
Describe the configuration of the bent wire
To find the magnetic field magnitude at point P, we can use the Biot-Savart Law. The Biot-Savart Law states that the magnetic field produced by a current-carrying wire at a point in space is proportional to the current and inversely proportional to the distance from the wire.
The formula for the magnetic field at a point due to a straight wire is given by:
B = (μ₀ * I) / (2π * r)
Where:
B = Magnetic field magnitude
μ₀ = Permeability of free space (4π * 10^(-7) T.m/A)
I = Current flowing in the wire
r = Distance from the wire to the point
Now, in the given scenario, we have a bent wire, but we can consider it as two straight wires carrying current in the same direction.
Since the current in both wires is 2 A and the distance from each wire to point P is the same (10 cm), we can calculate the magnetic fields produced by each wire separately using the formula mentioned above.
Then, we can find the net magnetic field at point P by adding the magnetic fields produced by both wires.
Therefore, the net magnetic field at point P can be calculated as follows:
B_net = B_wire1 + B_wire2
B_wire1 = (μ₀ * I) / (2π * r)
B_wire2 = (μ₀ * I) / (2π * r)
Substituting the values:
I = 2 A
r = 0.10 m (converted from 10 cm)
μ₀ = 4π * 10^(-7) T.m/A
B_wire1 = (4π * 10^(-7) * 2) / (2π * 0.10) T
B_wire1 = 2 * 10^(-6) T
B_wire2 = (4π * 10^(-7) * 2) / (2π * 0.10) T
B_wire2 = 2 * 10^(-6) T
B_net = B_wire1 + B_wire2
B_net = (2 * 10^(-6) + 2 * 10^(-6)) T
B_net = 4 * 10^(-6) T
Therefore, the magnetic field magnitude at point P is 4 * 10^(-6) Tesla.