As shown, four long straight wires are perpendicular to the page, and their cros

Question

As shown, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 6.20 cm. Each wire carries 18.0 A, and all the currents are out of the page. What is the net magnetic force per meter of wire length on the wire in the bottom left hand corner? Take the positive y direction as up and the positive x direction as to the right. What is the magnitude of the force per unit length?

What is the x component of the force per unit length?

What is the y component of the force per unit length?

Explanation / Answer

here,

a = 0.062 m

current , I = 18 A

the magnitude of net force in x direction = magnituce of net force in y direction , F = u0 * I^2 /( 2 * pi * a) + cos(45) * u0 * I^2 /( 2 * pi *1.41* a)

F = 1.26 * 10^-6 * 18^2/( 2 * pi * 0.062) + 1.26 * 10^-6 *cos(45)* 18^2/( 2 * pi * 0.062 * 1.41)

Fx = Fy= 1.57 * 10^-3 N

|F| = sqrt(Fx^2 + Fy^2)

|F| = 2.21 * 10^-3 N

the magnitude of the force per unit length
is 2.21 * 10^-3 N

the x component of the force per unit length is 1.57 * 10^-3 N

the y component of the force per unit length is 1.57 * 10^-3 N

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