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Field on the axis of a circular coil compared with the field at its centre

The same question, asked 3 times: 13 May 2024 S2, 16 Apr 2026 S2*, 19 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    13 May 2024 S2

    9
    A circular current carrying coil has radius RR. The magnetic induction at the centre of the coil is BcB_c. The magnetic induction of the coil at a distance 3R\sqrt{3}R from the centre along the axis is BAB_A. The ratio BA:BcB_A:B_c is

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  2. Question 2

    16 Apr 2026 S2

    133
    A circular loop of radius R is carrying current I. The ratio of magnetic field at the center of circular loop and at a distance R from the center of the loop on its axis is

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  3. Question 3

    19 Apr 2026 S2

    132
    A current carrying circular coil of radius 'R' produces magnetic field B1B_1 at an axial point P at a distance 'x' from its centre and B2B_2 at point Q placed at its centre respectively . If B2=8B1B_2 = 8B_1, the value of x is

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