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Physics · 2023 · 3 marks
CBSE 2023 · Region 4 · Set 2 · Q30
(a) Two coplanar concentric circular loops of radii R and r(≪ R) are arranged coaxially. Obtain the expression for their mutual inductance. (b) A…
(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
\[2 \mathrm{s}<t \leq 6 \mathrm{s} \quad \& 10 \mathrm{s} \leq t \leq 14 \mathrm{s}
\]
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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.