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MODEL PAPER 2 — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMODEL PAPER 23 Marks
Question
$i.$ Define the term self$-$inductance and write its $S.I.$ unit.
$ii.$ Obtain the expression for the mutual inductance of two long co$-$axial solenoids $S_1$ and $S_2$ wound one over the other, each of length $L$ and radii $r_1$ and $r_2$ and $n_1$ and $n_2$ number of turns per unit length, when a current $I$ is set up in the outer solenoid $S _2$.
✓

Answer

$i.$ Self$-$Inductance is the property by which an opposing induced emf is produced in a coil due to a change in current, or magnetic flux, linked with the coil.
$ii.$ In this question, a long co$-$axial solenoids $S_1$ and $S_2$ wound one over the other, each of length $L$ and radii $r_1$ and $r_2$ and $n_1$ and $n _2$ number of turns per unit length, when a current $I$ is set up in the outer solenoid $S _2$.
Image

Let a current $l_2$ flow in the secondary coil
$\therefore B _2=\frac{\mu_0 N_2 i_2}{t}$
$\therefore$ Flux linked with the primary coil $=\frac{\mu_0 N_2 N_1 A_1 i_2}{l}$
$= M _{12} i _2$
Hence, $M _{12}=\frac{\mu_0 N_2 N_1 A_2}{l}$
$\mu_0 n_2 n_1 A_1 l\left(n_1=\frac{N_1}{l} ; n_2=\frac{N_2}{l}\right)$

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