Mutual Induction PYQs: JEE Mains Physics

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1. 1. A circular current loop of radius \(R\) is placed inside square loop of side length \(L\) \((L >> R)\) such that they are co-planar and their centers coincide. The permeability of free space is \(\mu_0\). The mutual inductance between circular loop and square loop is _______. 2026 Hard
2. 2. Consider \(\mathrm{I}_1\) and \(\mathrm{I}_2\) are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If \(\mathrm{L}_1=\) self inductance of coil \(1, \mathrm{M}_{12}=\) mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be ________. 2025 Medium
3. 3. A small square loop of wire of side \(\ell\) is placed inside a large square loop of wire of side \(L\) \(\left(\mathrm{L}=\ell^2\right)\). The loops are coplanar and therr centers coinside. The value of the mutual inductance of the system is \(\sqrt{\mathrm{x}} \times 10^{-7} \mathrm{H}\), where X = _______. 2024 Hard
4. 4. Two coils have mutual inductance \(0.002 \ \mathrm{H}\). The current changes in the first coil according to the relation \(\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}\), where \(\mathrm{i}_0=5 \mathrm{~A}\) and \(\omega=50 \pi\) \(\mathrm{rad} / \mathrm{s}\). The maximum value of \(\mathrm{emf}\) in the second coil is \(\frac{\pi}{\alpha} \mathrm{V}\). The value of \(\alpha\) is_______. 2024 Hard
5. 5. Two conducting circular loops \(A \) and \(B\) are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is _______.
   2024 Hard
6. 6. Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' \(R\) ' is placed inside a large square loop of wire of side \(L\) \(( L \gg R )\). The loops are coplanar and their centres coincide :
   2023 Medium
7. 7. A small square loop of wire of side \(l\) is placed inside a large square loop of wire \(L(L \gg l)\). Both loops are coplanar and their centres coincide at point \(O\) as shown in figure. The mutual inductance of the system is.
   2022 Hard
8. 8. A small square loop of side \('a'\) and one turn is placed inside a larger square loop of side \({b}\) and one turn \((b \gg a)\). The two loops are coplanar with thei centres coinciding. If a current \(I\) is passed in the square loop of side \('b',\) then the coefficient of mutual inductance between the two loops is 2021 Hard
9. 9. There are two long co -axial solenoids of same length \(l.\) The inner and outer coils have radii \(r_1\) and \(r_2\) and number of turns per unit length \(n_1\) and \(n_2\) respectively. The ratio of mutual inductance to the self -inductance of the inner -coil is 2019 Hard
10. 10. Two coils \(P\) and \(Q\) are separated by some distance. When a current of \(3\, A\) flows through coil \(P\) a magnetic flux of \(10^{-3}\, Wb\) passes through \(Q\). No current is passed through \(Q\). When no current passes through \(P\) and a current of \(2\, A\) passes through \(Q\), the flux through \(P\) is 2019 Medium
11. 11. A small circular loop of wire of radius \(a\) is located at the centre of a much larger circular wire loop of radius \(b\). The two loops are in the same plane. The outer loop of radius \(b\) carries an alternating current \(I = I_0\, cos\, (\omega t)\) . The emf induced in the smaller inner loop is nearly 2017 Hard
12. 12. A circular loop ofradius \(0.3\ cm\) lies parallel to amuch bigger circular loop ofradius \(20\ cm\). The centre of the small loop is on the axis of the bigger loop. The distance between their centres is \(15\ cm\). If a current of \(2.0\ A\) flows through the smaller loop, then the flux linked with bigger loop is 2013 Medium
13. 13. Two coils, \(X\) and \(Y\), are kept in close vicinity of each other. When a varying current, \(I(t)\), flows through coil \(X\), the induced emf \((V(t))\) in coil \(Y\), varies in the manner shown here. The variation of \(I(t)\); with time, can then be represented by the graph labelled as graph
    2013 Medium

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