A long wire carrying a current I lies in the plane of a rigid rectangular loop carrying current h, parallel to its longer sides. (See leftmost Figure below. In this figure, choose the horizontal axis as your x-axis.) The rectangle has sides a and b as shown, and the wire is a distance d from the loop. (a) Find the magnitude and direction of the resultant force on the loop. col (viewed end-on) cable This arrangement is used in the design of a magnetically levitated train. Many vertical rectangular coils (N turns) are fixed in each carriage directly above a cable fixed to the track bed, as shown in the rightmost Figure. The coil

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Chapter1: Units, Trigonometry. And Vectors
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2. A long wire carrying a current I lies in the plane of a rigid rectangular loop carrying current I1, parallel to its longer
sides. (See leftmost Figure below. In this figure, choose the horizontal axis as your x-axis.) The rectangle has sides
a and b as shown, and the wire is a distance d from the loop. (a) Find the magnitude and direction of the resultant
force on the loop.
coil
(viewed end-on)
cable
This arrangement is used in the design of a magnetically levitated train. Many vertical rectangular coils (N turns)
are fixed in each cariage directly above a cable fixed to the track bed, as shown in the rightmost Figure. The coil
and carriage have the same length b. The carriage has weight per unit length w N/m. (b) When the dimensions d
and a are chosen such that a » d to minimize the power requirements (minimize the currents I and H), what should
be the requirement for w in terms of I and h? (c) If d =1 cm, w= 1000 N/m, and the trackbed cable and coil each
carry currents of 100 A, how many turns N would the coil need?
Transcribed Image Text:2. A long wire carrying a current I lies in the plane of a rigid rectangular loop carrying current I1, parallel to its longer sides. (See leftmost Figure below. In this figure, choose the horizontal axis as your x-axis.) The rectangle has sides a and b as shown, and the wire is a distance d from the loop. (a) Find the magnitude and direction of the resultant force on the loop. coil (viewed end-on) cable This arrangement is used in the design of a magnetically levitated train. Many vertical rectangular coils (N turns) are fixed in each cariage directly above a cable fixed to the track bed, as shown in the rightmost Figure. The coil and carriage have the same length b. The carriage has weight per unit length w N/m. (b) When the dimensions d and a are chosen such that a » d to minimize the power requirements (minimize the currents I and H), what should be the requirement for w in terms of I and h? (c) If d =1 cm, w= 1000 N/m, and the trackbed cable and coil each carry currents of 100 A, how many turns N would the coil need?
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