Force between an Infinitely Long Wire and a Square Loop A square loop of wire wi

Question

Force between an Infinitely Long Wire and a Square Loop A square loop of wire with side length a carries a current I_1. The center of the loop is located a distance d from an infinite wire carrying a current I_2. 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!) What is the magnitude, F, of the net force on the loop? Express the force in terms of I_1, I_2, a, d, and mu_0. The magnetic moment m of a current loop is defined as the vector whose magnitude equals the area of the loop times the magnitude of the current flowing in it {m = I A), and whose direction is perpendicular to the plane in which the current flows. Find the magnitude, F, of the force on the loop from in terms of the magnitude of its magnetic moment. Express F in terms of m, I_2, a, d, and mu_0.

Explanation / Answer

Here ,

part a)

for the net force on the loop

Fnet = Fleft - Fright

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

the net force on the loop is u0 * I2 * I1* a/(2pi) * (1/(d - a/2) - 1/(d + a/2))

part B)

magnetic moment , m = I1 * a^2

Now , for the magnetic force on the loop

Fnet = u0 * m * I2/(2pi * a)* (1/(d - a/2) - 1/(d + a/2))

the force on the loop is u0 * m * I2/(2pi * a)* (1/(d - a/2) - 1/(d + a/2))

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