A square frame made of a thin copper wire has initial side length

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A square frame ABCDABCD made of a thin copper wire has initial side length a=0.40 ma=0.40\,\text{m}. The frame is placed in a uniform magnetic field of magnitude B=0.25 TB=0.25\,\text{T} which is perpendicular to the plane of the frame and directed into the page. Starting from rest at t=0t=0, the point DD is pulled uniformly towards AA along ADAD so that the side length decreases at a constant rate of 2.0×10−2 m s−12.0\times10^{-2}\,\text{m\,s}^{-1}. The electrical resistance of the entire frame is 1.5 Ω1.5\,\Omega. (a) Obtain an expression for the side length s(t)s(t) of the frame at any time tt until the frame collapses completely. (b) Derive an expression for the induced emf ε(t)\varepsilon(t) in the frame as it collapses. (c) Hence obtain the induced current I(t)I(t) as a function of time and state its direction with respect to the original magnetic field. (d) Calculate the total energy dissipated as heat in the frame during the entire collapse process.

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