Final answer:
The force on a power line in a magnetic field is determined using the formula F = I x L x B x sin(θ), where I is the current, L is the length of the conductor, B is the strength of the magnetic field, and θ is the angle between the current and magnetic field direction. This force leads to practical concerns such as mechanical stress and safety hazards.
Step-by-step explanation:
The force on a 100-m section of DC power line for a light-rail system, which carries 1000 A at a 30.0° angle to the Earth's magnetic field of 5.00×10-5 T, can be calculated using the formula for the magnetic force on a current-carrying conductor: F = I × L × B × sin(θ), where:
- I is the current through the conductor,
- L is the length of the conductor within the magnetic field,
- B is the magnetic field strength,
- θ is the angle between the current direction and the magnetic field.
Substituting the given values into the formula gives us the force F = 1000 A × 100 m × 5.00×10-5 T × sin(30°) which calculates to a specific value that reflects the force on this section of the power line.
Practical concerns of such forces may include mechanical stresses on the power lines which can cause them to stretch, sway, or even snap, potentially leading to system instability or failure, as well as safety hazards for maintenance personnel and the public.