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We will use a video to study faraday’s law of electromagnetic induction by analyzing the induction that occurs due a coil of copper wire sliding along an air track that passes through an external magnetic field. specifically, we will: examine some of the main principles behind faraday’s law. apply lenz’s law to determine the direction of the induced emf. take measurements of the induced emf from the voltmeter as the coil passes into and out of the external magnetic field. use the horizontal scale provided to determine the speed of the coil. calculate the magnetic field induced in the coil as it passes into and out of the external magnetic field.

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.