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Two coils with a common centre in perpendicular planes: field at the centre

The same question, asked 3 times: 2 May 2023 S1*, 16 May 2023 S1*, 12 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S1

    38
    Two identical current carrying coils with same centre are placed with their planes perpendicular to each other. If current I=2 AI = \sqrt{2}\,\text{A} and radius of the coil is R=1 mR = 1\,\text{m}, then magnetic field at centre is equal to (μ0=\mu_0 = permeability of free space)

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  2. Question 2

    16 May 2023 S1

    24
    Two coils P and Q each of radius R carry currents I and 8I\sqrt{8}I respectively in same direction. Those coils are lying in perpendicular planes such that they have a common centre. The magnitude of the magnetic field at the common centre of the two coils is (μ0=\mu_0 = permeability of free space)

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  3. Question 3

    12 May 2024 S1

    22
    Two similar coils each of radius RR are lying concentrically with their planes at right angles to each other. The current flowing in them are II and 2I2I. The resultant magnetic field of induction at the centre will be (μ0=\mu_{0}= Permeability of vacuum)

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