Question

You know that the net magnetic force on the (closed) current loop in the uniform magnetic field is zero. As shown in the figure below, the rectangular thin wire loop running current 12=8.45 A is, however, in the non-uniform magnetic field produced by a long straight wire carrying current 11=13.88 A. The rectangular loop and the source wire are in the same (xy)-plane with the geometrical dimensions illustrated in the figure and equal to a=0.96 cm, b=2 cm and c=67 cm. . a b Find Cartesian components Fx and Fy of the net magnetic force F exerted on the rectangular loop: mN. mN, Fy=1 What is the magnitude of the flux B, DA =) of the magnetic field of the source wire through the surface bounded by the rectangular loop?: Bl= G.cm2 (Since the magnetic field is not uniform over the surface of the loop, you do need to integrate over the area.)

Answer 1

F_net,y = 0 mN

because force on upper and lower sides are equal in magnitude and opposite in direction

_______________

B1 = u_o I1 / 2$\pi$a = 4$\pi$e-7 * 13.88 / 2$\pi$ * 0.96e-2

and

F1 = I2 LB1

F1 = 1.637e-3 N

and

B2 = u_o I1 / 2$\pi$(a + b) = 9.378e-5 T

so,

F2 = 5.31e-4 N

so,

Fnet,x = 1.106 mN

____________________________

1 weber = 100000000 G.cm²

flux = integral ( B.dA)

flux = (u_o I1 c / 2$\pi$) ln ( a + b / a)

flux = 2.094e-6 Wb

so,

flux = 209.4 G.cm²