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The ratio of magnetic field at the centre of the ring of radius R to the point on the axis at a distance 2√2 R from its centre is ________.

Asked in GUJCET 2025 · Centre and axis of a loop

• (1) 27 : 1
• (2) 81 : 1
• (3) 1 : 9
• (4) 1 : 2√2

Step-by-step solution

Why the other options are wrong

• (2) 81:1 comes from raising R²+x² to the power 2 instead of 3/2: ((9R²)/(R²))²=81. The axial field carries (R²+x²)^3/2 in its denominator.
• (3) 1:9 is the ratio turned round and with the power dropped to 1: (R²)/(R²+x²)=1/9. The centre field is the larger of the two, so the ratio asked for must exceed 1.
• (4) 1:2√2 treats the axial field as falling like 1/x, as for a straight wire, so that the ratio would simply be R:x. On the axis of a loop the field falls far faster — like 1/(x³) once x R.

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