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JEE Main 201911 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
11 January
Shift
Morning Shift
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2019 · 11 January · Morning Shift · Physics · Electromagnetic Induction

There are two long co-axial solenoids of same length l . The inner...

There are two long co-axial solenoids of same length ll. The inner and outer coils have radii r1r_{1} and r2r_{2} and number of turns per unit length n1\mathrm{n}_{1} and n2\mathrm{n}_{2}, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is :

Options

  1. An1n2\frac{n_{1}}{n_{2}}
  2. Bn2n1⋅r1r2\frac{n_{2}}{n_{1}} \cdot \frac{r_{1}}{r_{2}}
  3. Cn2n1⋅r22r12\frac{n_{2}}{n_{1}} \cdot \frac{r_{2}^{2}}{r_{1}^{2}}
  4. Dn2n1\frac{n_{2}}{n_{1}}

Correct answer

D. n2n1\frac{n_{2}}{n_{1}}

Step-by-step solution

The rate of mutual inductance is given by M=μ0n,n2πr12…(i)\mathrm{M}=\mu_{0} \mathrm{n}, \mathrm{n}_{2} \pi \mathrm{r}_{1}^{2} \quad \ldots(\mathrm{i})The rate of self inductance is given by L=μ0n12πr12…(ii)\mathrm{L}=\mu_{0} \mathrm{n}_{1}^{2} \pi \mathrm{r}_{1}^{2} \quad \ldots(\mathrm{ii}) Dividing (i) by (ii) ⇒ML=n2n1\Rightarrow \frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}
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