(c) If x is the difference between r and R0and x is much smaller than R0, use Taylor's expansion to show that F is proportional to x and derive the force constant k in terms of A and b.

5.A rectangular loop with width L and a slide wire of mass m are as shown in the figure. A uniform magnetic field B is directed perpendicular to the plane of the loop into the plane of the figure. The slide wire is given an initial speed of U0at t = 0 and then released. There is no friction between the slide wire and the loop, and the resistance of the loop is negligible in comparison to the resistance R of the slide wire.(a) Obtain an expression for F, the magnitude of the force exerted on the slide wire while it is moving at speed u. (b) Find the speed u(t) and displacement x(V) in terms of B, I, m, R and u0. (c) Find the maximum distance the slide wire moves. (d) What is the total energy consumed by the resistance R? (20%)

題組內容

(c) If x is the difference between r and R₀and x is much smaller than R₀, use Taylor's expansion to show that F is proportional to x and derive the force constant k in terms of A and b.

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