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Romantic Getaway

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What is the magnetic field at the center of a circular loop that has two semi circles carrying current. Well it is zero! We first find the field at point C due to the straight wires that are carrying current and then due to each semi circle. The field due to first straight wire is zero because we find that the angle between any element ds on this straight wire and unit vector r pointing towards C is zero and therefore dB contribution from each current element is zero. The same is true for the second wire as well. For the semi circle, we use the right hand rule where we mentally grasp the semi circle our right hand, with the thumb in the direction of the current. Then the fingers curl around the wire and enter into the screen at C . The field B is directed perpendicular into the plane at C. Using the same right hand rule for the other semi circle, the field vector points out of the screen at C. Since the current is same in both semi circle, the two vectors cancel each other. So the total field at the center of this set up is zero
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