A current loop having two circular arc is as shown in fig and carries a current of 10A . The magnetic field at point O is (N π /14)× 10- 7T . Then find N..

Question

A current loop having two circular arc is as shown in fig and carries a current of 10A . The magnetic field at point O is (N π /14)× 10- 7T . Then find N.. <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-yaecv0jyu2hrbew2.jpg" /> (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

overset arrow B0 = overset arrow BP Q+ overset arrow BQ R+ overset arrow BR S+ overset arrow BS P = overset arrow 0+((μ )0 I/4 π r1)((π /3)) hatk+ overset arrow 0+((μ )0 I/4 π r2)((π /3))(.- hatk.) =(μ 0/12)[(1/r1) - (1/r2)] hatk =(4 π × 10- 7 × 10/12)[(1/4 × 10- 2) - (1/7 × 10- 2)] =(4 π × 10- 7 × 10/12 × 10- 2)[(7 - 4/4 × 7)]=(5 π /14)× 10- 7T

Q. A current loop having two circular arc is as shown in fig and carries a current of 10A . The magnetic field at point O is 14Nπ​×10−7T . Then find N..

B→0​ =B→PQ​+B→QR​+B→RS​+B→SP​ =0→+4πr1​(μ)0​I​(3π​)k^+0→+4πr2​(μ)0​I​(3π​)(−k^) =12μ0​​[r1​1​−r2​1​]k^ =124π×10−7×10​[4×10−21​−7×10−21​] =12×10−24π×10−7×10​[4×77−4​]=145π​×10−7T

Q. A current loop having two circular arc is as shown in fig and carries a current of $10 A$ . The magnetic field at point $O$ is $\frac{N π}{14} \times 1 0^{- 7} T$ . Then find N..