two long, parallel lines each carry 100-A currents are 20 cm apart.
1) calculate the magnetic field at the point C that is 5 cm to the left from the left wire.
2) calculate the magnetic field at the point C that is 5 cm to the right from the left wire.
3) calculate the magnetic field at the point C that is 5 cm to the right from the right wire.
x <-------------> x
20 cm
To calculate the magnetic field at a given point due to two parallel current-carrying wires, we can use the Biot-Savart Law. This law states that the magnetic field (B) at a point due to a current-carrying wire is directly proportional to the current (I) in the wire and inversely proportional to the distance (r) from the wire.
The formula to calculate the magnetic field at a point due to a straight current-carrying wire is given by:
B = (μ₀ * I) / (2π * r)
Where:
B = Magnetic field
μ₀ = Permeability of free space (a constant equal to 4π x 10^-7 Tm/A)
I = Current in the wire
r = Distance from the wire
Now, let's calculate the magnetic fields at the given points:
1) To calculate the magnetic field at point C, 5 cm to the left from the left wire:
Since we are interested in the left wire, the distance (r) will be 15 cm, and the current (I) will be 100 A.
B1 = (μ₀ * I) / (2π * r)
B1 = (4π x 10^-7 Tm/A * 100 A) / (2π * 0.15 m)
2) To calculate the magnetic field at point C, 5 cm to the right from the left wire:
Since we are still interested in the left wire, the distance (r) will be 25 cm, and the current (I) will be 100 A.
B2 = (μ₀ * I) / (2π * r)
B2 = (4π x 10^-7 Tm/A * 100 A) / (2π * 0.25 m)
3) To calculate the magnetic field at point C, 5 cm to the right from the right wire:
Since we are now interested in the right wire, the distance (r) will be 5 cm, and the current (I) will be 100 A.
B3 = (μ₀ * I) / (2π * r)
B3 = (4π x 10^-7 Tm/A * 100 A) / (2π * 0.05 m)
By simplifying these equations, you can calculate the magnetic fields at the respective points.