An infinitely long straight wire carries a current $i_{1} = 1 amp$ . A rectangular current loop placed in the same plane of shown dimensions carries a current $i_{2} = 1 amp$ anticlockwise. Magnitude of net force on the loop is found to be $β \frac{μ _{0}}{4 π}$ . Find value of $β$ .

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Ans (1.00) F n e t ​ = F 1 ​ − F 2 ​ = i 2 ​ B 1 ​ ( 2 a ) − i 2 ​ B 2 ​ ( 2 a ) = ( 4 π μ 0 ​ ​ 2 a 2 i 1 ​ ​ ) i 2 ​ ( 2 a ) − ( 4 π μ 0 ​ ​ 4 a 2 i 1 ​ ​ ) i 2 ​ ( 2 a ) = 4 π 2 μ 0 ​ ​ − 4 π μ 0 ​ ​ = 4 π μ 0 ​ ​ ∴ β = 1

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