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Suppose in the figure that the four identical currents i = 29 A, into or out of

ID: 1460663 • Letter: S

Question

Suppose in the figure that the four identical currents i = 29 A, into or out of the page as shown, form a square of side 70 cm. What is the force per unit length (magnitude and direction) on the wire in the bottom left hand corner? (N/m) 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?

I know similar questions have been posted before, but no matter what I do, I cannot get the correct answer. Please walk me through this in a detailed way if you can, I'm trying to understand it.

Explanation / Answer

magnetic field is, B2 = B4 =0*I/2a = 8.285*10-6 T
the magnetic field, B3 = B2*cos45 =5.858*10-6 T
magneti field B caused by four identical currents:
Horizontal field:

Bx = B2-B3*cos45 = 4.14e-6 T
Vertical field:

By = B2 + B3*cos45 = 1.24e-5 T
Net magnetic field is,

B = (Bx2+By2) = 1.31*10-5 T

The net force per unit length is,

F/L = B*i =1.31*10-5 *29 =  3.8*10-4 N/m
y-coponent: Fy = Bx*i = 4.14e-6 *29 = 1.2e-4 N/m, along +y axis
x-component: Fx= -By*I= -1.24e-5*29 = -3.596e-4 N/m ; along -x-axis