I have seen this question posted but I don\'t understand why the net magnetic fi

Question

I have seen this question posted but I don't understand why the net magnetic field is B(outer loop) - B(inner loop) or how to find the direction. Can someone please explain so I can understand the concept here? Thanks! 10. Two circular current-carrying loops of wire are shown in the drawing. The inner loop has a radius of R,and carries a current I,, while the outer loop has a radius of 2R, and carries a current of 41. The currents are in opposite directions. If R, 0.20 m and I 2.1 A, determine the magnitude and direction of the net magnetic field at the center of the two loops.

Explanation / Answer

due to inner loop,

B1 = u0 I0 / (2 pi R0) into the page

due to outer loop,

B2 = u0 (4 I0) / (2 pi (2 R0)) = u0 I0 / pi R0 out of page

B = B2 - B1 = u0 I0 / (2 pi R0)

B = (4pi x 10^-7 x 2.1) / (2 pi 0.20)

B = 2.1 x 10^-6 T Or 2.1 uT  

out of page

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