Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B 1 , at its centre when a current I passes

Question

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B 1 ​ , at its centre when a current I passes through it. The ratio B 1 ​ : B 2 ​ is:

TestHub · Accepted Answer

For loop B = 2 a μ 0 ​ nI ​ where, a is the radius of loop. Then, B 1 ​ = 2 a μ 0 ​ I ​ Now, for coil B = 4 π μ 0 ​ I ​ ⋅ x 3 2 nA ​ at the centre x = radius of loop B 2 ​ ∴ B 1 ​ : B 2 ​ = 1 : 3 ​ = 4 π μ 0 ​ ​ ⋅ ( a /3 ) 3 2 × 3 × ( I /3 ) × π ( a /3 ) 2 ​ = 2 a μ 0 ​ ⋅ 3 I ​ B 2 ​ B 1 ​ ​ = μ 0 ​ ⋅ 3 I /2 a μ 0 ​ I /2 a ​ ​

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