Question

In the figure, a long straight wire carries a current i₁ = 26.8 A and a rectangular loop carries current i₂ = 28.2 A. Take a = 0.765 cm, b = 9.11 cm, and L = 37.9 cm. What is the magnitude of the net force on the loop due to i₁?

Answer 1

force exerted on top side of loop

F1 = (uo / 4pi) 2 i1 i2 * L / a

force exerted on bottom side of loop

F2 = (uo/ 4pi) 2 i1 i2 * L / ( a + b)

now due to symmetry of fifmgure, force exerted on right and left side of loop must be equal and opposite hence they cancel each other so the resultance force is given by the vector sum of F1 and F2

F = F1 - F2

F = 10^-7 * 2 * 26.8* 28.2* ( 1 / 0.765 - 1 / ( 0.765 + 9.11))* 10^2* 0.379

F = 6.908* 10^-3 N

directed upwards

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