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BITSAT 2024Paper 2

Exam: BITSAT
Year: 2024
Paper: Paper 2
Subject: Physics
Chapter: Electromagnetic Induction

BITSAT 2024 · Paper 2 · 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

l

. The inner and outer coils have radii

r_1

and

r_2

and number of turns per unit length

n_1

and

n_2

, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is:

Options

A $\frac{n_1}{n_2}$
B $\frac{n_2}{n_1} \cdot \frac{n_1}{r_2}$
C $\frac{n_2}{n_1} \cdot \frac{r_2^2}{r_1^2}$
D $\frac{n_2}{n_1}$

Correct answer

D. $\frac{n_2}{n_1}$

Step-by-step solution

The rate of mutual inductance is given by

\mathrm{M}=\mu_0 \mathrm{n}_1 \mathrm{n}_2 \pi \mathrm{ m}_1^2

....(i) The rate of self inductance is given by

\mathrm{L}=\mu_0 \mathrm{n}_1^2 \pi \mathrm{r}_1^2

.....(ii) Dividing (i) by (ii)

\Rightarrow \frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{n}_2}{\mathrm{n}_1}

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