Bar Magnet & Dipole Field
Magnetic moment m = pole-strength × 2ℓ; field lines emerge from N, end at S.
Key Notes
A bar magnet is a permanent magnet with two opposite POLES at its ends — by convention North (N) and South (S).
Magnetic field lines emerge from N, curve around, and enter S externally. Inside the magnet they go S → N (closed loops, no monopoles).
Magnetic dipole moment: m = NIA (for a current loop equivalent) or m = qm × 2L for a magnetic-charge bar magnet.
Field along the AXIAL line (on the magnet's axis, distance r ≫ L): B_axial = (μ₀/4π)·(2m/r³).
Field along the EQUATORIAL line (perpendicular bisector, distance r ≫ L): B_equatorial = (μ₀/4π)·(m/r³). Half the axial field.
Like poles repel, unlike attract — force ∝ 1/r⁴ for short bar magnets along axial line.
Cutting a bar magnet in half produces TWO smaller bar magnets, each with its own N and S — NO isolated monopoles.
Earth itself acts as a giant bar magnet (approximately) — used in compass navigation.
Formulas
Magnetic dipole moment
For a current loop. Units: A·m².
Axial field (far)
Along the magnet's axis, r ≫ L.
Equatorial field (far)
On perpendicular bisector — HALF of axial.
Torque in external B
Aligns m parallel to B; basis of compass.
Potential energy
Minimum at θ = 0 (aligned).
Important Points
Magnetic field lines are CONTINUOUS closed loops — no monopoles (Gauss's law for magnetism: ∮B·dA = 0).
Cutting a magnet doesn't isolate poles. Always end up with two magnets.
B_axial : B_equatorial = 2 : 1 at the same distance.
Magnetic moment is a VECTOR — pointing S → N inside the magnet.
Field of a bar magnet outside resembles that of a current loop of equivalent moment.
Common pitfall: thinking 'poles' are real point particles — they're not. They're an effective description.
Bar Magnet & Dipole Field notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.