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What is the magnitude of the equatorial fields due to a bar magnet of length 5.0 cm at a distance 75 cm from its mid point ? The magnetic moment of the bar magnet is 0.75 A m².

Asked in GUJCET 2021 · Field of a bar magnet and earth's field

• (1) 3.2×10⁻⁷ T
• (2) 1.78×10⁻⁷ T
• (3) 6.4×10⁻⁷ T
• (4) 3.56×10⁻⁷ T

Step-by-step solution

Why the other options are wrong

• (1) Neither the equatorial nor the axial formula gives 3.2×10⁻⁷ T with these numbers. Sanity check: (μ₀)/(4π)m/(r³)=((10⁻⁷)(0.75))/((0.75)³)=1.78×10⁻⁷ T, and twice that on the axis.
• (3) This is option 1 doubled, and no route with m=0.75 A m² at r=0.75 m reaches it: even the axial field is only 3.56×10⁻⁷ T.
• (4) This is the axial (end-on) field, (μ₀)/(4π)(2m)/(r³)=3.56×10⁻⁷ T -- exactly twice the equatorial field the question asks for.

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