Chapter 28, Problem 44AP

You have been called in as an expert witness in a civil case. The case involves a dispute between neighbors. The plaintiff neighbor is complaining about a buzzing noise during the night that prevents the plaintiff from sleeping. He claims that the buzzing is coming from a light fixture on the defendant’s porch ceiling. The defendant likes to do installations and repairs himself and has done a sloppy job of installing the light fixture. The fixture hangs vertically from a single wire that is attached through the porch ceiling and down the wall to one connector in a nearby electrical outlet. The second wire is hung horizontally with strings at the level of the light and then runs down the wall to the other connector in the outlet. The defendant leaves the light on all night long for security. Recalling his high school physics, the plaintiff states that the combination of the 60-Hz household voltage and the magnetic field of the Earth results in an oscillating driving force on the single wire from which the light fixture hangs vertically. This, in turn, sets up a standing wave in the wire, and that is the cause of the buzz. You have been hired by the defense attorney. Upon hearing the details of the case, you obtain permission from the defendant and make measurements. The mass of the light fixture is 17.5 kg. The vertical wire from which it hangs is 0.150 m long and has a mass of 0.030 kg. Is the plaintiff correct that the magnetic field of the Earth is causing the buzzing of the wire? Ignore any effect of the second wire.