CBSE 2025 · Region 4 · Set 3 · Q24 · 3 marks
(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?
(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 $\displaystyle 1$, $\displaystyle \frac{\varepsilon}{d I / d t}=L$, is more for coil $\displaystyle 1$ than coil 2.
Electromagnetic InductionInductanceApplyshort_answermedium
More from Electromagnetic Induction
- Assertion: The mutual inductance between two coils is maximum when the coils are wound on each other. Reason…2024 · asked 3×
- In the process of charging of a capacitor, the current produced between the plates of the capacitor is:2023 · asked 3×
- A vertically held bar magnet is dropped along the axis of a copper ring having a cut as shown in the diagram.…2025 · asked 3×
- The direction of induced current in the loop abc is:2023 · asked 3×
- (i) Define self-inductance of a coil. Derive the expression for the energy required to build up a current I…2025 · asked 3×
- Two coils C 1 and C 2 are placed close to each other. The magnetic flux φ 2 linked with the coil C 2 varies…2023 · asked 3×
- Assertion: Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more.…2026 · asked 3×
- (i) State Lenz's law and explain how this law is a consequence of conservation of energy principle. (ii) A…2025 · asked 3×
CBSE Class 12 Physics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.