A horizontal overhead power line carries a current of 500A in west to east direction. What is the magnetic field 1.5m below? What is it's direction?
To determine the magnetic field at a point below a current-carrying power line, we can use Ampere's law. Ampere's law states that the magnetic field around a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.
To calculate the magnetic field at a point 1.5 meters below the power line, we need to use the following equation:
B = (μ₀ * I) / (2π * d)
Where:
- B represents the magnetic field
- μ₀ (mu naught) is the permeability of free space, which is approximately 4π * 10^-7 T·m/A
- I is the current flowing through the wire
- d is the distance from the wire
Using the given values:
- I = 500A (current in the wire)
- d = 1.5m (distance below the wire)
- μ₀ = 4π * 10^-7 T·m/A (permeability of free space)
Plugging in the values, we get:
B = (4π * 10^-7 T·m/A * 500A) / (2π * 1.5m)
Simplifying and canceling out common terms, we find:
B = (2 * 10^-4 T·m) / (1.5m)
B ≈ 0.000133 T
Therefore, the magnetic field 1.5m below the power line is approximately 0.000133 Tesla (T).
To determine the direction of the magnetic field, we need to use the right-hand rule. If the current is flowing from west to east, we can wrap our right hand around the wire such that our fingers curl in the direction of the current. The direction of the magnetic field can be determined by the direction your thumb naturally points. In this case, since the current is flowing from west to east, the magnetic field will circle counterclockwise around the wire when viewed from above. Therefore, the magnetic field at a point 1.5m below the power line will flow in the counterclockwise direction.