A bar magnet is of length (size) l. The ratio of its equatorial field and axial field for the same distance r (where r l) is .

Question

Accepted Answer

(1) 0.5. Idea: for a short magnet (r l) the two standard results at distance r from the centre are Bₐₓᵢₐₗ=(μ₀)/(4π)(2m)/(r³) and B_eq=(μ₀)/(4π)m/(r³). Everything but the factor 2 is common to the two, so it cancels in the ratio: (B_eq)/(Bₐₓᵢₐₗ)=1/2=0.5. Where the 2 comes from: on the axis the pulls of the near and the far pole act along the same line and add, while on the equatorial line the two contributions are equal and tilted, and only their components parallel to the magnet survive. So the ratio of the equatorial field to the axial field is 0.5.

A bar magnet is of length (size) l. The ratio of its equatorial field and axial field for the same distance r (where r l) is ______ .

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