Question

5. Biot-Savart Law Shown in the figure below is a circular loop of current. Your job is to use the Biot-Savart Law to determine the magnetic field at the point P. Perhaps you find case poor artistic skills leave you uncertain, then the following short paragraph might lelp. the figure familiar and easy to interpret... REAT, just solve it. In The portiou of the loop that is closest to you is drawn as a solid are. The portion of the loop that is farthest from you (i.e. bchind the page) is drawn as a dashed are. The current is dowuward on the part of the loop closest to yor and upward on the portion farthest from you. Thus, the current at the "top of the loop" is toward you (pointerd out of the page) and the current at the "bottom of the loop" is away from you (pointed into the page). "top of the loop" "bottom of the loop" (a) Draw arrows on the figure to indicate each of the following i. (3 pts) The field contribution at P due to the top of the loop (label as dBtop). ii. (3 pts) The field contribution at P due to the botom of the loop (label as dB bottom). iii. (2 pts) The total field at point P (label as Btotal). (b) (12 pts) Integrate over the full loop to find Btotal

Answer 1

In delta POC we can write (using pythogoras theorem) (OC)^2 + (PO)^2 = PC^2 Let PC = r = > PC = squareroot a^2 + z^2 Let PC = r r = squareroot a^2 + z^2 Consider a small element all at the top, then Magnetic field due to this small current element Idl Vector, at Point P is dB Vector_rop = mu_0/4 r I dl Vector times r Vector/r^3 Answer part a(i) dB_Top = u_0/4 r I dl r sin theta/r^3 [theta rightarrow angle between I dl Vector nad r Vector] for small radius �a� as compared to distance z theta almostequalto 90 degree = > dB_Top = u_0/4 r I dl/r^2 = > dB_Top = u_0/4 r I dl/(a^2 + z^2) 1 Answer part a(i) Use Right hand thumb rule to find direction of dB at point P due to current element I dl Vector Similarly magnetic field at P due to current element

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