We make a loop of radius R by bending a cylindrical shape conductor cable of radius r << R and put it into a magnetic field of induction B perpendicular to its plane. Then we uniformly decrease B to zero in τ time. How much does this circular conductor heat up if its conductivity is σ, its massdensity is ρ, and its coecient of specific heat is c?

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter4: Nonlinear Oscillations And Chaos
Section: Chapter Questions
Problem 4.13P
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We make a loop of radius R by bending a cylindrical shape conductor cable of radius r << R and put it into a magnetic field of induction B perpendicular to its plane. Then we uniformly decrease B to zero in τ time. How much does this circular conductor heat up if its conductivity is σ, its massdensity is ρ,
and its coecient of specific heat is c?

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