JEE/NEET Physics · Magnetism & Matter series · Part 2 of 4 · All parts →
- A dipole in field B feels torque: τ = mB sinθ — it twists toward alignment
- Potential energy: U = −mB cosθ — lowest when aligned (stable), highest when opposed
- Work to flip from aligned to anti-aligned: W = 2mB
- Oscillations: a disturbed dipole swings — the basis of magnetometers
- Axial vs equatorial field of a bar magnet: B_ax = μ₀2m/4πr³, B_eq = μ₀m/4πr³ (half, reversed)
Why does a compass swing north? Its dipole moment sits in Earth’s field, feels a twist toward alignment, and — overshooting — oscillates like a pendulum until friction stills it. That gentle dance measures magnetic fields. Part 2 of the Magnetism & Matter series.
- The alignment torque
- Energy of orientation
- The oscillating needle
- The bar magnet’s own field
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
The Alignment Torque
Field B pushes the N-pole one way, the S-pole the other: a twisting couple, exactly like the current loop of the last series:
Energy of Orientation
The Oscillating Needle
Nudge a compass from north and the restoring torque swings it back — past, and back again: simple harmonic-ish oscillation with period T = 2π√(I/mB) (I = needle’s rotational inertia). Time the swings and you’ve measured B: the oscillation magnetometer.
The Bar Magnet’s Own Field
| Position | Field | Compare |
|---|---|---|
| Axial (on the N-S line) | μ₀ 2m / 4πr³ | strongest far-field |
| Equatorial (⊥ bisector) | μ₀ m / 4πr³ | half the axial, reversed |
| Both | fall as 1/r³ | dipole fields fade fast |
Solved Examples
τ = 0.5 × 0.2 = 0.1 N·m.
✔
Answer: 0.1 N·m
W = 2mB = 2 × 0.5 × 0.2 = 0.2 J.
✔
Answer: 0.2 J
T = 2π√(I/mB) → B = 4π²I/(mT²) = 4π²×2×10⁻⁶/(4×10⁻²×4) ≈ 5×10⁻⁵ T.
Earth-scale field, measured with a stopwatch.
✔
Answer: ≈5×10⁻⁵ T
- U = +mB cosθ sign error. Energy is MINUS m·B: aligned (θ=0) must be the lowest state.
- Torque maximum at alignment. Opposite: aligned torque is zero (stable), perpendicular is maximum.
- Equatorial field direction. It points OPPOSITE to m at the equator — a favourite direction question.
- Using 1/r² for dipole fields. Dipoles fall as 1/r³: unlike single charges or poles, distant dipole fields fade fast.
This Physics in Your Daily Life
- Every compass ever carried — dipole torque aligning with Earth’s field: navigation by τ = mB sinθ for two millennia.
- Magnetic knife racks and cabinet latches — aligned dipoles locking into energy valleys: U = −mB as furniture.
- Magnetic stirrers in labs — rotating fields torquing dipole stir bars: chemistry stirred by alignment energy.
- Magnetometers in phones (compass apps) — oscillation and alignment physics miniaturised into chips: orientation sensing.
- MRI’s radio flips — nuclear dipoles lifted over the 2mB energy hill by resonant pulses: medical imaging as dipole acrobatics.
A weather vane in wind: pressure differences twist it until it points downwind, but momentum carries it past, and it wobbles back — swinging until it settles. A magnetic dipole in a field is an electromagnetic weather vane: torque toward alignment, inertia overshooting, oscillation born.
m = 0.5 A·m² in Earth’s 5×10⁻⁵ T: flip energy 2mB = 5×10⁻⁵ J — tiny, yet enough to line up every compass needle on the planet. In an MRI’s 3 T: 3 J per mole-scale nuclear moments — radio-frequency photons must be supplied to climb the hill: resonance imaging.
Draw the dipole as an arrow in a set of field lines: parallel to the field, it sits in an energy valley (U = −mB); perpendicular, halfway up (U = 0); anti-parallel, on the hilltop (U = +mB). Tip it slightly and the torque arrow always points back downhill: the energy landscape IS the restoring force.
Practice set (answers hidden — try first)
(NEET-level) m = 0.2 A·m² at 30° to B = 0.5 T: τ =
(JEE Main-level) U for m aligned with B (m=0.1, B=0.3):
(NEET-level) Torque when dipole ⊥ B is
(Concept) Stable equilibrium for a dipole:
(JEE Main-level) Axial vs equatorial field at same r:
- τ = mB sinθ toward alignment
- U = −mB cosθ; flip cost 2mB
- oscillation: T = 2π√(I/mB)
- axial 2× equatorial, 1/r³ falloff
- energy valley at alignment
- 🔁 torque and energy formulas
- 🔁 stability of alignment
- 🔁 oscillation timing method
- 🧠 Chant: ‘align to the valley’.
- 🧠 Measure trick: ‘time the swings, read the field’.
- 🏠 Daily: compass apps run dipole oscillation physics.
- 🏠 Daily: MRI flips nuclear dipoles over 2mB hills.
Quick revision
- A dipole in field B feels torque: τ = mB sinθ — it twists toward alignment
- Potential energy: U = −mB cosθ — lowest when aligned (stable), highest when opposed
- Work to flip from aligned to anti-aligned: W = 2mB
- Oscillations: a disturbed dipole swings — the basis of magnetometers
- Axial vs equatorial field of a bar magnet: B_ax = μ₀2m/4πr³, B_eq = μ₀m/4πr³ (half, reversed)
- The bar magnet’s own field
Have a doubt on this topic?
