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Physics · 2025 · 3 marks
CBSE 2025 · Region 4 · Set 3 · Q24
(a) Obtain an expression for the self-inductance of a long solenoid of length ' l ', cross-sectional area 'A' and having ' N ' turns. (b) The figure…
(a)
Obtain an expression for the self-inductance of a long solenoid of length ' $\displaystyle l$ ', cross-sectional area 'A' and having ' N ' turns.
(b)
The figure shows the plot of magnitude of induced emf ( $\displaystyle \varepsilon$ ) versus the rate of change of current in two coils ' $\displaystyle 1$ ' and ' $\displaystyle 2$ '. Which coil has greater value of self-inductance and why?
Marking-scheme solution
(a)
Magnetic field due to a current I flowing in the solenoid: $\displaystyle B=\mu_{0} n I$
Total flux linked with solenoid is:
$\displaystyle N \phi_{B}=(n l)\left(\mu_{0} n I\right) A$
$\displaystyle =\mu_{0} n^{2} A l I$
$\displaystyle L=\frac{N \phi_{B}}{I}$
$\displaystyle L=\mu_{0} n^{2} A l$
(b)
Coil 1.
Slope of line 1, $\displaystyle \frac{\varepsilon}{d I / d t}=L$, is more for coil $\displaystyle 1$ than coil 2.
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