A long wire carrying current I is parallel to the longer sides of a rigid rectangular loop carrying current I1. The rectangle has the sides a and b shown, and the wire is d away from the loop. (a) Determine the magnitude and direction of the net force on the loop. This configuration is used to create a magnetically levitated train. Each carriage has many vertical rectangular coils (N turns) fixed directly above a cable fixed to the track bed. Both the coil and the carriage are the same length b. The carriage weighs w N/m per unit length. (b) If the dimensions d and an are chosen so that a » d to minimize power requirements (minimize currents I and I1), what should the requirement for w be in terms of I and I1? (c) Given d = 1 cm, w = 1000 N/m, and trackbed cable and coil carrying currents of 100 A each, how many turns N would the coil require?
A long wire carrying current I is parallel to the longer sides of a rigid rectangular loop carrying current I1. The rectangle has the sides a and b shown, and the wire is d away from the loop.
(a) Determine the magnitude and direction of the net force on the loop.
This configuration is used to create a magnetically levitated train. Each carriage has many vertical rectangular coils (N turns) fixed directly above a cable fixed to the track bed. Both the coil and the carriage are the same length b. The carriage weighs w N/m per unit length.
(b) If the dimensions d and an are chosen so that a » d to minimize power requirements (minimize currents I and I1), what should the requirement for w be in terms of I and I1?
(c) Given d = 1 cm, w = 1000 N/m, and trackbed cable and coil carrying currents of 100 A each, how many turns N would the coil require?
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