Lesson 5 of 11 · 6 min
The electrostatic analog
NCERT §5.2.4
Nisha puts a small compass 10 cm from her 0.4 A m² magnet, first on its axis and then on its perpendicular bisector. The needle swings harder on the axis. By how much, and which way does it point each time?
The lesson in notes
In short
The far field of a bar magnet of moment m follows from the electric dipole's field by swapping E → B, p → m and 1/(4πε₀) → μ₀/4π.
On the axis, at distance r much larger than the magnet's size l: B_A = (μ₀/4π)(2m/r³), along m.
On the equatorial line (the normal bisector), for r ≫ l: B_E = −(μ₀/4π)(m/r³), half the axial size at the same distance and pointing opposite to m.
Both fall off as 1/r³: doubling the distance cuts the field to one-eighth.
The dipole analogy runs through the table: 1/ε₀ ↔ μ₀, p ↔ m, torque p × E ↔ m × B, energy −p·E ↔ −m·B.
Example 5.2: a needle Q near a needle P is in equilibrium only when m_Q is parallel or antiparallel to P's field at Q. Parallel is stable, antiparallel unstable, and the lowest energy comes with Q on P's axis, pointing along P's field there, where that field is twice its equatorial size.