Magnetic Field using Bio’s Sievert law

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"Ans. 1The length of the edge of wire, a ,The flow of current in the loop, iSo, the current by the loop on the z ? axis, In the above diagram, first we calculate the magnetic field produced by the singlewire in the loop and after that multiply by fou..

"Ans. 1The length of the edge of wire, a ,The flow of current in the loop, iSo, the current by the loop on the z ? axis, In the above diagram, first we calculate the magnetic field produced by the singlewire in the loop and after that multiply by four to calculate the complete amount ofthe magnetic field. The magnetic field is a vector quantity,So calculate the magnetic field by the single edge of the loop,Consider a point P as shown in the figure, and take a unit length from the edge,So,The magnetic field produced by the unit length,Apply the Bio’s Sievert law, ? I(dl ?r) ?I ?dL ?sin ? dB() r ? ? ? 32 44 ??rr ?? I ?dL ?sin ? I x dB() r ? ? ?dx ? 23 44 ??rr a/2 a/2 ?? I dx I?? x dB() r?? ?? ? 2 2 3/2 2 2 2 1/2 ?a/2 4?? (x?? R ) 4 R (x R ) ?? ?a/2 ?I B ? (cos ? ? Cos ? ) 12 4 ?x Substitute the value of cos ? and cos ? in the above equation by applying the1 2 Pythagoras theorem of trigonometry,So,2 a 2 xz??4 Hence,aa /2 cos ? ? cos ? ? ?12 2 2 2 2 x?? a / 4 4x a Substitute the value in the above equation, ?? ?Ia 2 B ? ?? 22 4 ?x 4xa ? ?? ?Ia B ? 22 2 ?x 4xa ? The above expression is for single edge only so the total magnetic field by the loop,?I a a BB ? 4 sin ? ? 4 ? t 2 22 2 ? 22 ?? 42ax ? 4xa ? ?? 2 4 ?Ia B ? t 2 2 2 2 ? (4x?? a ) 4x 2a Hence Proved. "

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