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Two circular coils from the same wire, one of twice the radius: ratio of potential differences for equal fields at the centres

The same question, asked 4 times: May 2021 S1, 14 May 2024 S1, 13 May 2026 S2, 15 May 2026 S1. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    May 2021 S1

    17
    Two circular coils A and B are made from the same wire but the radius of coil A is twice that of coil B. If the magnetic fields at their centres are the same, then the ratio of potential differences applied across A to that of B is

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  2. Question 2

    14 May 2024 S1

    11
    Two circular coils made from same wire but radius of 1st^{st} coil is twice that of 2nd^{nd} coil. If magnetic field at their centres is same then ratio of potential difference applied across them is (1st^{st} to 2nd^{nd} coil)

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  3. Question 3

    13 May 2026 S2

    131
    Two circular coils AA and BB are made from the same wire but the radius of coil AA is twice that of coil BB. What is the ratio of potential difference applied across them, so that the magnetic field at their centres is the same?

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  4. Question 4

    15 May 2026 S1

    132
    Two circular coils A and B are made from same wire but the radius of coil A is twice that of coil B. If the magnetic field at their centres is same then the ratio potential difference applied across them is

    Tap an option to check your answer.