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Physics · 2023 · 3 marks
CBSE 2023 · Region 4 · Set 1 · Q27
(a) The figure shows the variation of induced emf as a function of rate of change of current for two identical solenoids X and Y. One is air cored…
(a)
The figure shows the variation of induced emf as a function of rate of change of current for two identical solenoids X and Y . One is air cored and the other is iron cored. Which one of them is iron cored? Why ?
(b)
Obtain an expression for self-inductance of a long solenoid of length L and cross-sectional area A having N turns.
Marking-scheme solution
(a)
X is iron cored.
Reason- From the graph-
\[\text { Slope of the graph }=\frac{\varepsilon}{|d I / d t|}=L
\]
Slope of X is more than that of Y. Hence X is iron cored because Inductance of iron cored coil is more than that of air cored coil.
(b)
Magnetic field due to solenoid (axis)
\[B=\frac{\mu_{0} N I}{l}
\]
Magnetic flux through the solenoid
\[\phi_{B}=N \phi=\frac{\mu_{0} N^{2} A}{L} I
\]
Since self-inductance \(\displaystyle =\frac{\phi_{B}}{I}\)
\[=\frac{\mu_{0} N^{2} A}{L}
\]
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CBSE Class 12 Physics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.