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Mutual inductance of a small square loop inside a large coplanar square loop

The same question, asked 3 times: 2021 Paper 22*, 25 Jul 2022*, 31 Jan 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 22

    10
    A small square loop of side 'a' and one turn is placed inside a larger square loop of side bb and one turn (b>>a)(b> >a). The two loops are coplanar with their centres coinciding. If a current II is passed in the square loop of side ' bb ', then the coefficient of mutual inductance between the two loops is :

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  2. Question 2

    25 Jul 2022

    13
    A small square loop of wire of side ll is placed inside a large square loop of wire L(L>>l)L(L > > l). Both loops are coplanar and their centres coincide at point OO as shown in figure. The mutual inductance of the system is:

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  3. Question 3

    31 Jan 2024

    27
    A small square loop of wire of side ll is placed inside a large square loop of wire of side LL (L=l2)\left( L = l^{2} \right). The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is x×10−7H\sqrt{x}\times10^{- 7}H, where x=x = _____ .