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Electromagnetic Induction question

2021 · Q169
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Electromagnetic Induction question

2021 · Q169

NEETPhysicsElectromagnetic InductionMCQ+4 / −1
Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to :
  1. A
    R22R1{{R_2^2} \over {{R_1}}}R1​R22​​
  2. B
    R1R2{{{R_1}} \over {{R_2}}}R2​R1​​
  3. C
    R2R1{{{R_2}} \over {{R_1}}}R1​R2​​
  4. D
    R12R2{{R_1^2} \over {{R_2}}}R2​R12​​
View written solutionFree

Correct answer: A

Two concentric coils are of radius R1 and R2 as shown

NEET 2021 Physics - Electromagnetic Induction Question 7 English Explanation

Let current in outer loop be i

Magnetic field at center = B = μ0i2R1{{{\mu _0}i} \over {2{R_1}}}2R1​μ0​i​

Magnetic flux through inner coil = B ×\times× πR22\pi R_2^2πR22​

⇒\Rightarrow⇒ ϕ\phi ϕ = μ0i2R1×πR22{{{\mu _0}i} \over {2{R_1}}} \times \pi R_2^22R1​μ0​i​×πR22​

As per definition, ϕ\phi ϕ = Mi

⇒\Rightarrow⇒ M = (μ0π2)R22R1\left( {{{{\mu _0}\pi } \over 2}} \right){{R_2^2} \over {{R_1}}}(2μ0​π​)R1​R22​​

∴\therefore∴ M ∝\propto∝ R22R1{{R_2^2} \over {{R_1}}}R1​R22​​

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