Problem 2
A rod of length ℓ moves at speed v perpendicular to itself and uniform field B, closing a circuit through R. Neglect rod resistance. Find emf, current, and magnetic drag. Use the stated ideal model: quantities are constant or vary only as specified, with no extra drag, losses, or external influences. State a sign convention, keep units consistent, and use a classical approximation only where appropriate. (a) Set up the governing equation from a fundamental law. (b) Solve for the requested quantity under the stated conditions. (c) Check the result using a suitable limit, sign, or unit test, and report both the expression and its physical meaning.
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problems.proof.analysis
Choose the physical system and sign convention specified in the problem, then identify the ideal assumptions. This fixes which forces, currents, or quantities can be exchanged during the process.