MIT6_013S09_pset04

# MIT6_013S09_pset04 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.013 – Electromagnetics and Applications Problem Set 4 (six problems) Suggested Reading: Course notes, Sections 5.5.1, 6.1, 6.3, 5.3.1; 5.6, 4.3.1, 4.3.2; 1.3, 4.5.1-4.5.4, 5.2, 4.4.1-4.4.2; 2.3.2-2.3.4 Problem 4.1 (See associated lab instructions) A pill magnet of diameter D and area A = π D 2 /4 produces a nearly uniform magnetic field B o across its broad face. We wish to estimate B o using two different methods: induced voltage and force measurement. (a) When the magnet is dropped down a tightly fitting but slippery non- conducting cylinder it induces a voltage V(t) across a compact coil of N turns wrapped around the cylinder, as illustrated. Based on this illustrated data, what is the approximate value of B o ? Briefly explain your method and indicate which pole is North (top or bottom). Hint: Before drop, coil flux linkage Λ = 0. Between t = 0 and t o : ΔΛ NB o A. v(t) = d Λ /dt. V(t) V max V max /2 t o t t o - τ + - V(t) D Magnet, B o Insulating tube (b) What happens when this magnet is dropped down a copper cylinder? Why? (c) To measure the attraction of the magnet to a thin high-permeability steel plate, the magnet is taped to a digital scale that is preloaded with a large weight.

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