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Field on the axis of a circular coil

This type of question, asked 7 times: 13 May 2024 S2, 25 Apr 2025 S2, 16 Apr 2026 S2, 19 Apr 2026 S1, 19 Apr 2026 S2, 14 May 2026 S1, 19 May 2026 S2. All 7 questions 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

    25 Apr 2025 S2

    45
    A circular coil carrying current ' T ' has a radius ' rr ' and ' nn ' turns. The magnetic field along the axis of a coil at a distance ' 22r2\sqrt{2}r ' from its centre is (μ0=\mu_{0}= permeability of free space, nn is very small)

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  3. Question 3

    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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  4. Question 4

    19 Apr 2026 S1

    132
    Two circular coils X (smaller) and Y (bigger), each having a single turn, carry equal currents in the same direction and subtend the same angle at point 'O' along the axis of the coil. The distances of the centers of coil to point 'O' are dd and (d2)\left(\dfrac{d}{2}\right) for coil Y and X respectively. The radii of coils Y and X are (2r)(2r) and (r)(r) respectively. The magnetic induction due to the bigger coil at point 'O' is ByB_y and that due to smaller coil X at point 'O' is BxB_x. (d≫r)(d \gg r) The relation between BxB_x and ByB_y is

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  5. Question 5

    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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  6. Question 6

    14 May 2026 S1

    133
    The magnitude of magnetic induction at a point on the axis at a large distance rr from a centre of a circular coil of nn turns and area AA carrying current ii is (μ0\mu_0 = permeability of free space)

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  7. Question 7

    19 May 2026 S2

    132
    Consider a circular loop (radius RR) carrying current II, the magnetic field produced by it at a point on the axis at a distance zz from the centre of the loop is xR2(z2+R2)3/2\dfrac{xR^2}{(z^2 + R^2)^{3/2}}. The value of xx is

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