A circular loop of radius r of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field B at its centre. If instead, a circular loep of radius 2 r , made o

Question

A circular loop of radius r of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field B at its centre. If instead, a circular loep of radius 2 r , made of same material, having the same cross-section is connected to the same voltage source, what will be the magnetic ficld at its centre?

TestHub · Accepted Answer

B = 2 μ 0 ​ ​ ⋅ r I ​ ∵ I 1 ​ = R 1 ​ V ​ Case (I) l 1 ​ = 2 π r (length of the loop). R 1 ​ = ρ A l 1 ​ ​ and B 1 ​ = 2 μ 0 ​ ​ ⋅ r I 1 ​ ​ Case (II) I 2 ​ = 2 π ⋅ 2 r = 2 l 1 ​ R 2 ​ = ρ ⋅ A l 2 ​ ​ = ρ ⋅ A 2 l 1 ​ ​ = 2 R 1 ​ I 2 ​ = R 2 ​ V ​ = 2 R 1 ​ V ​ = 2 I 1 ​ ​ B 2 ​ = 2 μ 0 ​ ​ ⋅ 2 r I 2 ​ ​ = 2 μ 0 ​ ​ ⋅ 2 ⋅ 2 r I 1 ​ ​ ​ From Eqs. (i) and (ii), B 1 ​ B 2 ​ ​ = 2 μ 0 ​ ​ ⋅ r I 1 ​ ​ 2 μ 0 ​ ​ ⋅ 2 ⋅ 2 r I 1 ​ ​ ​ = 4 1 ​ Magnetic field B 2 ​ = 4 B 1 ​ ​

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