The magnetic field at the centre of a current carrying circular loop of radius R is 16 μT. The magnetic field at a distance x = √3R on its axis from the centre i $s ______$ μT.
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Question

The magnetic field at the centre of a current carrying circular loop of radius R is 16 μT. The magnetic field at a distance x = √3R on its axis from the centre i s ______ μT.

G1 Physics · Accepted Answer

Magnetic field at the centre of a circular loop is B₀ = μ₀I/(2R) = 16 μT. At axial distance x, B(x) = μ₀IR²/ [2(R²+x²)³ᐟ²]. Given, x = √3R. Therefore, R²+x² = R²+3R² = 4R². Hence, B(x) = μ₀IR²/ [2(4R²)³ᐟ²] = μ₀IR²/ [2×8R³] = μ₀I/(16R). Now, B(x)/B₀ = [μ₀I/(16R)]/ [μ₀I/(2R)] = 1/8. Therefore, B(x) = 16/8 = 2 μT. Correct option: C.