(a) A 13.0 m long, thin, uniform metal rod slides north at a speed of 29.0 m/s. The length of the rod maintains an east-west orientation while sliding. The vertical component of the Earth's magnetic field at this location has a magnitude of 36.0 μT. What is the magnitude of the induced emf between the ends of the rod (in mV)? Consider an electron in the rod in static equilibrium. What are the magnitudes of the electric and magnetic forces on the electron in terms of the electric and magnetic fields? If the electron is in equilibrium, what's true about the forces? What then is the electric field? From the electric field and the length, what is the emf? mV (b) What If? The east end of the rod impacts and sticks to a pylon, causing the rod to rotate clockwise as viewed from above. While the rod rotates, what is the magnitude of the induced emf between the ends of the rod (in mV)? (Hint: use conservation of angular momentum to find the speed of the rod after the collision.) x

(a) A 13.0 m long, thin, uniform metal rod slides north at a speed of 29.0 m/s. The length of the rod maintains an east-west orientation while sliding. The vertical component of the Earth's magnetic field at this location has a magnitude of 36.0 μT. What is the magnitude of the induced emf between the ends of the rod (in mV)? Consider an electron in the rod in static equilibrium. What are the magnitudes of the electric and magnetic forces on the electron in terms of the electric and magnetic fields? If the electron is in equilibrium, what's true about the forces? What then is the electric field? From the electric field and the length, what is the emf? mV (b) What If? The east end of the rod impacts and sticks to a pylon, causing the rod to rotate clockwise as viewed from above. While the rod rotates, what is the magnitude of the induced emf between the ends of the rod (in mV)? (Hint: use conservation of angular momentum to find the speed of the rod after the collision.) x

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

(a) A 13.0 m long, thin, uniform metal rod slides north at a speed of 29.0 m/s. The length of the rod maintains an east-west orientation
while sliding. The vertical component of the Earth's magnetic field at this location has a magnitude of 36.0 µT. What is the magnitude
of the induced emf between the ends of the rod (in mV)?
Consider an electron in the rod in static equilibrium. What are the magnitudes of the electric and magnetic forces on the electron in
terms of the electric and magnetic fields? If the electron is in equilibrium, what's true about the forces? What then is the electric field?
From the electric field and the length, what is the emf? mv
(b) What If? The east end of the rod impacts and sticks to a pylon, causing the rod to rotate clockwise as viewed from above. While the
rod rotates, what is the magnitude of the induced emf between the ends of the rod (in mV)? (Hint: use conservation of angular
momentum to find the speed of the rod after the collision.)
Given the formula for the emf from part (a), can you construct a formula for the emf of an infinitesimal slice of the rod in terms of
radial distance from the pivot and angular speed? Integrating this, what is the emf in terms of angular speed and length? What is the
initial angular momentum of the rod (based on its center of mass speed) about the pivot point? What is the final angular momentum
as it rotates (based on the moment of inertia of a rod rotating at one end)? Use this to find the final angular speed, and therefore final
emf. mV
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