Unit of Bohr magneton is ______.

Asked in GSEB Board March 2020 · Magnetic moment of loops and charges

Answer: (4) A m²

Step-by-step solution

Given: the Bohr magneton, the magnetic moment of an electron in the first Bohr orbit.

Idea: whatever its value, it is a magnetic dipole moment, and a magnetic moment is current times area, m=IA.

Units: [A]×[m²]=A m².

The same follows from μ_B=(eℏ)/(2mₑ), whose SI unit is J T⁻¹, and J T⁻¹=A m².

(1) Charge times area. A magnetic moment is current times area, and current is charge per second, so the unit must carry the ampere, not the coulomb.
(2) Current times length — the unit of the current element I d⃗l in the Biot-Savart law. A moment needs an area, so the metre is squared.
(3) Current per unit area, which is current density. The moment multiplies by the area, so the metre carries the power +2, not -2.

More Torque on a Current Loop and Magnetic Dipole Moment questions

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