Two parallel wires carry 1-A currents in unknown directions. The distance between the wires is 10-cm. What is the magnitude of the magnetic field B in Teslas at a point P located 6-cm away from the axis of one of the wires and 8-cm away from the axis of the other wire?
Unot=4pi×10^-7
To find the magnitude of the magnetic field 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 is directly proportional to the current and inversely proportional to the distance from the wire.
The formula for the magnetic field produced by a straight current-carrying wire is given by:
B = (μ0 * I) / (2 * π * r)
Where:
B is the magnetic field
μ0 is the permeability of free space, given as 4π × 10^-7 T·m/A
I is the current in the wire
r is the distance from the wire
In this case, we have two parallel wires carrying 1-A currents in unknown directions. The distance between the wires is 10-cm. We need to find the magnetic field at point P, which is located 6-cm away from the axis of one wire and 8-cm away from the axis of the other wire.
To calculate the magnetic field at point P, we need to consider the contributions from both wires.
Let's calculate the magnetic field produced by each wire separately and then add them up:
For the first wire:
B1 = (μ0 * I1) / (2 * π * r1)
where I1 is the current in the first wire, and r1 is the distance of point P from the axis of the first wire (6-cm).
Similarly, for the second wire:
B2 = (μ0 * I2) / (2 * π * r2)
where I2 is the current in the second wire, and r2 is the distance of point P from the axis of the second wire (8-cm).
Now, we can calculate the magnetic field at point P by adding the contributions from both wires:
B = B1 + B2
Substituting the given values:
B = (μ0 * I1) / (2 * π * r1) + (μ0 * I2) / (2 * π * r2)
Finally, plug in the values of I1, I2, r1, r2, and μ0 to find the magnitude of the magnetic field B at point P.