Let B P and B Q be the magnetic field produced by the wire P and Q which are placed symmetrically in a rectangular loop ABCD as shown in the figure. Current in wire P is I directed inward and in Q

Question

Let B P ​ and B Q ​ be the magnetic field produced by the wire P and Q which are placed symmetrically in a rectangular loop ABCD as shown in the figure. Current in wire P is I directed inward and in Q is 2I directed outward. Values of line integral of magnetic induction for different segments of loop ABCD are given as Find the current I (in A)

TestHub · Accepted Answer

2 π μ 0 ​ ​ × 2 I [ 2 tan − 1 ( L − x y ​ ) ] 4 π μ 0 ​ ​ × I [ tan − 1 ( y L − x ​ ) + tan − 1 ( y x ​ ) ] = 2 μ 0 ​ 2 π μ 0 ​ I ​ ( 2 tan − 1 ( x y ​ ) ) = μ 0 ​ I tan − 1 ( x y ​ ) = π I tan − 1 ( y x ​ ) + tan − 1 ( y L − x ​ ) = 4 π I tan − 1 ( L − x y ​ ) = π ⇒ I = 6 A

Physics - Magnetism Question with Solution | TestHub

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