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. col " (viewed end-on) cable This arrangement is used in the design of a magnetically levitated train. Many vertical rectangular coils (N tums) are fixed in each carriage 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 I1), what should be the requirement for w in terms of I and ? (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?

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. col " (viewed end-on) cable This arrangement is used in the design of a magnetically levitated train. Many vertical rectangular coils (N tums) are fixed in each carriage 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 I1), what should be the requirement for w in terms of I and ? (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?