KA18: Ch 29c Force between an Infinitely Long Wire and a Square Loop ? 3017 ? Ex

Question

KA18: Ch 29c Force between an Infinitely Long Wire and a Square Loop ? 3017 ? Express the force in terms of 11, 12, a, d, and Ao View Available Hint(s) A square loop of wire with side length a carries a current I1. The center of the loop is located a distance d from an infinite wire carrying a current I2. The infinite wire and loop are in the same plane; two sides of the square loop are parallel to the wire and two are perpendicular as shown. (Figure 1) Submit Part B The magnetic moment m of a current loop is defined as the vector whose magnitude equal:s the area of the loop times the magnitude of the current flowing in it (m = 1A), and whose direction is perpendicular to the plane in which the current flows. Find the magnitude, F, of the force on the loop from Part A in terms of the magnitude of its magnetic moment. Figure 1 of 1 Express F in terms of m, 12, a, d, and Ao Submit wire loop Wire Provide Feedback Next >

Explanation / Answer

a)Fnet = F1 - F2

F1 = u0 I1 I2 a/2 pi (d - a/2)

F2 = u0 I1 I2 a/2 pi (d + a/2)

Fnet = u0 I1 I2 a/2 pi (d - a/2) - u0 I1 I2 a/2 pi (d + a/2)

Fnet = u0 I1 I2 a/2 pi (1/(2d - a) - 1/(ad + a))

Fnet = 2 u0 a I1 I2/pi (4d^2 - a^2)

b)m = IA ; A = a^2

F = 2 u0 I2/pi (4d^2 - a^2)

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