CBSE 2023 · Region 4 · Set 2 · Q30 · 3 marks
(a)Two coplanar concentric circular loops of radii $\displaystyle R$ and $\displaystyle r(\ll R)$ are arranged coaxially. Obtain the expression for their mutual inductance.(b)A square loop of side $\displaystyle 20$ cm starts moving at t $\displaystyle =0$ with a velocity of $\displaystyle 5 \mathrm{~cm} / \mathrm{s}$ towards a region of uniform magnetic field as shown in the figure. Specify the time interval(s) during which induced emf is produced in the loop.
(a)
Two coplanar concentric circular loops of radii $\displaystyle R$ and $\displaystyle r(\ll R)$ are arranged coaxially. Obtain the expression for their mutual inductance.
(b)
A square loop of side $\displaystyle 20$ cm starts moving at t $\displaystyle =0$ with a velocity of $\displaystyle 5 \mathrm{~cm} / \mathrm{s}$ towards a region of uniform magnetic field as shown in the figure. Specify the time interval(s) during which induced emf is produced in the loop.
Marking-scheme solution
(a)
Magnetic field due to current I flowing in the loop with radius R, at its centre.
\[B=\frac{\mu_{0} I}{2 R}
\]
Magnetic flux linked with the smaller coil
\[\phi=\frac{\mu_{0} I}{2 R} . \pi r^{2}
\]
which is equal to MI
hence \(\displaystyle M=\frac{\mu_{0} \pi r^{2}}{2 R}\)
(b)
\(\displaystyle t=\frac{l}{v}\)
Induced e.m.f. during time interval
\[2 \mathrm{s}<t \leq 6 \mathrm{s} \quad \& 10 \mathrm{s} \leq t \leq 14 \mathrm{s}
\]
Electromagnetic InductionInductanceApplyshort_answerhard
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CBSE Class 12 Physics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.