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Physics · 2024 · 3 marks
CBSE 2024 · Region 4 · Set 1 · Q28
(a) (i) Define mutual inductance. Write its SI unit. (ii) Derive an expression for the mutual inductance of a system of two long coaxial solenoids of…
(a)(i)
Define mutual inductance. Write its SI unit.
(ii)
Derive an expression for the mutual inductance of a system of two long coaxial solenoids of same length $\displaystyle l$, having turns $\displaystyle \mathrm{N}_{1}$ and $\displaystyle \mathrm{N}_{2}$ and of radii $\displaystyle \mathrm{r}_{1}$ and $\displaystyle \mathrm{r}_{2}\left(>\mathrm{r}_{1}\right)$.
OR
(b)
What are ferromagnetic materials ? Explain ferromagnetism with the help of suitable diagrams, using the concept of magnetic domain.
Marking-scheme solution
(a)
(i)
Mutual inductance between two coils is defined as the magnetic flux associated with a coil when unit current flows through the neighbouring coil.
OR
Mutual inductance between two coils is defined as the magnitude of induced emf in a coil when the rate of change of current in the neighbouring coil is unity.
SI unit of mutual inductance is henry (H).
When current $\displaystyle I_{2}$ flows in the outer solenoid, the resulting flux linkage with the inner solenoid:
$\displaystyle N_{1} \phi_{1}=N_{1} B_{2} A_{1}$
$\displaystyle N_{1} \phi_{1}=N_{1}\left(\frac{\mu_{0} N_{2} I_{2}}{l}\right) \pi r_{1}^{2}$
$\displaystyle N_{1} \phi_{1}=\frac{\mu_{0} N_{1} N_{2} \pi r_{1}^{2} I_{2}}{l}$ ………………………($\displaystyle 1$)
$\displaystyle N_{1} \phi_{1}=M_{12} I_{2}$ ……………………… ($\displaystyle 2$)
From equations ($\displaystyle 1$) and ($\displaystyle 2$):
$\displaystyle M_{12}=\frac{\mu_{0} N_{1} N_{2} \pi r_{1}^{2}}{l}$
Ferromagnetic substances are those which get strongly magnetised when placed in an external magnetic field.
In the absence of an external magnetic field, domains are randomly oriented and the substance exhibits weak magnetisation.
In the presence of an external magnetic field, domains orient themselves in the direction of the magnetic field and the substance exhibits strong magnetisation.
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CBSE Class 12 Physics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.