Consider a circular loop of wire of radius r carrying current I .We wish to calculate its magnetic field at the center O. The entire loop can be divided into a large number of small current elements.
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| Magnetic field at the center of a circular current loop |
Consider a current element dl of the loop. According to Bio-Severt law, the magnetic field at the center O due to this element is
The field at point O points normally into the plane of paper, as shown by enclosed cross ⊗.The direction of dl is along the tangent, so dl⊥r . Consequently, the magnetic field at the center O due to this current element is
The magnetic field due to all such current elements will point into the the plane of paper at center O. Hence the total magnetic field at the center O is
