A pair of long, rigid metal rods, each of length 0.50 m,

Chapter 28, Problem 28.78

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A pair of long, rigid metal rods, each of length 0.50 m, lie parallel to each other on a frictionless table. Their ends are connected by identical, very lightweight conducting springs with unstretched length l0 and force constant k (Fig. P28.78). When a current I runs through the circuit consisting of the rods and springs, the springs stretch. You measure the distance x each spring stretches for certain values of I. When I = 8.05 A, you measure that x = 0.40 cm. When I = 13.1 A, you find x = 0.80 cm. In both cases the rods are much longer than the stretched springs, so it is accurate to use Eq. (28.11) for two infinitely long, parallel conductors. (a) From these two measurements, calculate l0 and k. (b) If I = 12.0 A, what distance x will each spring stretch? (c) What current is required for each spring to stretch 1.00 cm?