Kevin Zhou — USAPhO Practice D Problem 5 · Kevin Zhou #USAPhOD.5
Physics · electromagnetism
Problem
Under what conditions are the oscillations of the block almost entirely simple harmonic?
Question B2
Thetechnologicalandscientifictransformationsduringthe19th centuryproducedacompellingneed
foruniversallyacceptedstandardsfortheelectricalquantities. Itwasthoughtthenewabsoluteunits
should only rely on the standards of length, mass and time established after the French Revolution.
An intensive experimental work to settle the values of these units was developed.
Lord Kelvin devised the following setup in the 1860s to set the absolute standard for the ohm.
4
Kevin Zhou Physics Olympiad Handouts
A closedcircularcoilofN turns, radius a, andresistance R is rotatedwithconstantangularvelocity
ω about a vertical diameter in a horizontal magnetic field B = B xˆ. A small magnetic needle is
0 0
placed at the center of the coil. It is free to turn slowly around the zˆ axis in a horizontal plane, but
it cannot follow the rapid rotation of the coil.