Practice question
Question
A bar magnet with original \( m = 1.6 \, \text{A m}^2 \) is cut transversely into two equal parts. What
is \( m \) of each part?
Explanation
**Field due to bar magnet** on axial line is B_axial = (μ₀/4π)·2m/r³, equatorial B_eq = (μ₀/4π)·m/r³, where μ₀/4π = 10⁻⁷ T·m/A, m magnetic moment (A·m²), r distance (m). Axial field twice equatorial at same distance and parallel to moment, equatorial opposite to moment direction. When cut transversely, each part has half the original magnetic moment. Given: m = 1.6 A m² . Each part: m' = (1.6/2) = 0.8 A m² . Substituting values gives 0.8 A m², which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.
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