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Mutual inductance of two concentric coplanar loops (small loop at the centre of a large one)

The same question, asked 12 times: 4 May 2023 S2*, 10 May 2023 S2*, 10 May 2024 S1, 10 May 2024 S2*, 11 May 2024 S1*, 19 Apr 2025 S1, 20 Apr 2025 S1*, 15 Apr 2026 S2*, 16 Apr 2026 S2, 17 Apr 2026 S2*, 12 May 2026 S1*, 19 May 2026 S2. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    4 May 2023 S2

    4
    The planar concentric rings of metal wire having radii r1r_1 and r2r_2 (with r1>r2r_1 > r_2) are placed in air. The current II is flowing through the coil of larger radius. The mutual inductance between the coils is given by (μ0=\mu_0 = permeability of free space)

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  2. Question 2

    10 May 2023 S2

    41
    Two concentric circular coils having radii 'r1r_1' and 'r2r_2' (r2≪r1r_2 \ll r_1) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (μ0\mu_0 = permeability of free space) (Both coils have single turn)

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  3. Question 3

    10 May 2024 S1

    45
    Two conducting circular loops of radii R1R_1 and R2R_2 are placed in the same plane with their centres coinciding. If R1>R2R_1 > R_2, the mutual inductance MM between them will be directly proportional to

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  4. Question 4

    10 May 2024 S2

    36
    Two concentric circular coils having radii r1r_1 and r2r_2 (r2≪r1)(r_2\ll r_1) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, μ0=\mu_0= permeability of free space)

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  5. Question 5

    11 May 2024 S1

    1
    A coil of radius rr is placed on another coil (whose radius is RR and current flowing through it is changing) so that their centres coincide (R≫r)(R \gg r). If both the coils are coplanar then the mutual inductance between them is (μ0\mu_0 = permeability of free space)

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  6. Question 6

    19 Apr 2025 S1

    23
    Two conducting circular loops of radii R1R_{1} and R2R_{2} are placed in the same plane with their centres coinciding. If R1>R2R_{1}>R_{2}, the mutual inductance M between them will be directly proportional to

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  7. Question 7

    20 Apr 2025 S1

    34
    Two planar concentric rings of metal wire havin radii r1r_{1} and r2(r1>r2)r_{2}\left( r_{1}>r_{2} \right) are placed in air. Thi current I am flowing through the coil of large radius. The mutual inductance between the coils is given by ( μ0=\mu_{0}= permeability of free space)

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  8. Question 8

    15 Apr 2026 S2

    135
    Two concentric circular coils having radii r1r_1 and r2r_2 (r2<<r1)(r_2 << r_1) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, μ0\mu_0 = permeability of free space)

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  9. Question 9

    16 Apr 2026 S2

    134
    A circular coil of radius 'r' is placed on another circular coil whose radius is 'R' and the current flowing through it is changing and their centers coincide. (R≫r)(R \gg r). If both the coils are coplanar, then the mutual inductance between them is proportional to

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  10. Question 10

    17 Apr 2026 S2

    134
    Two planar concentric rings of metal wire having radii 'r1r_1' and 'r2r_2' (with r1>r2r_1 > r_2) are placed in air. The current 'I' is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( μ0\mu_0 = permeability of free space)

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  11. Question 11

    12 May 2026 S1

    136
    Two conducting circular loops of radii rr and 2r2r are placed in the same plane with their centres coinciding. The mutual inductance MM between them is {same current is passing through both the coils} (μ0\mu_0 = permeability of free space)

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  12. Question 12

    19 May 2026 S2

    135
    Two conducting circular loops of radii r1r_1 and r2r_2 are placed in the same plane with their centres coinciding. If r1>>r2r_1 >> r_2, then the mutual inductance MM between them is proportional to [I1=I_1 = current flowing through coil 1 and I2=I_2 = current flowing through coil 2]

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