The magnetic field has been measured to be horizontal everyw

The magnetic field has been measured to be horizontal everywhere along a rectangular path x = 23 [cm] and y = 4 [cm] high, as shown in the figure above. Along the bottom, the average magnetic field B_1 = 1.6 Times 10^-4 [T], along the sides, the average magnetic field B_2 = 0.9 Times 10^-4 [T], and along the top the average magnetic field B_3 = 0.4 Times 10^-4 [T]. What can you conclude about the electric currents in the area that is surrounded by the rectangular path (What is the magnitude of the current)? I = 12 [A] I = 22 [A] I = 6.4 [A] I = 10/2 [A]

Solution

from ampere\'s law,

Integral of B.dL = u0 Iinside

(B1 - B3) x + B2 y - B2y = u0 Iinside

((1.6 - 0.4) x 10^-4 ) (0.23) = (4pi x 10^-7) Iin

Iin = 21.96 A Or 22 A

Ans( 22 A)