JEE/NEET Physics · Moving Charges & Magnetism series · Part 8 of 8 · All parts →
- Eight parts on one card — force, motion, selectors, fields, laws, meters
- F = qvB sinθ · r = mv/qB · T = 2πm/qB · v = E/B
- Biot-Savart wire: μ₀I/2πr · solenoid: μ₀nI · Ampere: ∮B·dl = μ₀I
- Wire force: BIl · pair: μ₀I₁I₂/2πd · torque: NIAB sinθ
- Right-hand rules everywhere: force, grip, and circulation
The final card of the Moving Charges & Magnetism series — eight parts on one revision sheet, plus the century of machines this chapter unleashed.
- The master formula card
- The one-rule-per-part recap
- The motor age
- Final practice set
- Recap
The Master Formula Card
| What | Formula | Remember |
|---|---|---|
| Charge force | F = qvB sinθ | ⊥ always, no work |
| Radius | r = mv/(qB) | momentum meter |
| Period | T = 2πm/(qB) | speed-blind |
| Velocity selector | v = E/B | one speed passes |
| Cyclotron f | qB/(2πm) | fixed tune |
| Wire field | B = μ₀I/(2πr) | grip rule circles |
| Loop centre | μ₀NI/(2R) | concentrator |
| Solenoid | μ₀nI | n per metre |
| Ampere’s law | ∮B·dl = μ₀I_enc | count piercings |
| Wire force | F = BIl sinθ | parade pushed |
| Wire pair | μ₀I₁I₂/(2πd) | same = attract |
| Loop torque | NIAB sinθ | motor twist |
| Galvanometer | φ ∝ I | spring balance |
The One-Rule-Per-Part Recap
1: sideways-only force on movers. 2: circles, radius = momentum. 3: crossed fields gate one speed; cyclotrons climb by fixed tune. 4: currents weave circling fields. 5: circulation counts enclosed current. 6: wires feel each other’s weavings. 7: loops twist, springs measure.
The Motor Age
- From Oersted’s compass twitch (1820) to Faraday’s motor (1821) took ONE YEAR — this chapter’s discovery-to-machine speed remains physics’ fastest.
- The electrified twentieth century — motors in factories, trams in cities, pumps in fields: τ = NIAB turned electrical science into mechanical civilisation.
- Medical and research frontiers — MRI magnets, cyclotron therapy, particle colliders: Part 2 and 3 geometry saving lives and probing matter.
- Sensors everywhere — Hall probes, clamp meters, GFCI protectors: Amperean bookkeeping embedded in daily safety.
- Coming full circle to relativity — the tiny force between wires that Einstein couldn’t reconcile with Galilean physics opened the door to special relativity: this chapter asked the question that reshaped all of physics.
Electricity could only light and heat until it learned to TURN. Magnetism supplied the twist: a force that is always sideways is exactly what rotation needs. The day physics combined current loops with magnetic fields, wheels could be driven without steam — factories moved from rivers to sockets.
One loop: milli-newton-metres of torque. One hundred turns and 50 cm² later: newton-metres. Multiply by engineering decades: locomotive traction motors deliver mega-newton forces — the same NIAB sinθ, scaled by geometry and persistence.
See the chapter as one machine blueprint: current source (Battery series), field weaver (Biot-Savart/Ampere), force producer (qvB/BIl), rotor (loop torque), controller (commutator), measurement (galvanometer) — every part a wall in the house the motor built.
Practice set (answers hidden — try first)
(NEET-level) 1 μC at 10⁵ m/s ⊥ 0.4 T: F =
(JEE Main-level) r for a proton (v=10⁷, B=0.5):
(NEET-level) 3 m wire, 2 A, ⊥ 0.25 T: F =
(JEE Main-level) Same-direction parallel currents:
(NEET-level) Solenoid B with n=1000/m, I=1 A ≈
- F = qvB sinθ and F = BIl
- circles: r = mv/qB, T = 2πm/qB
- fields: wire, loop, solenoid, Ampere
- pair force and loop torque
- meters by shunt and multiplier
- 🔁 the 13-row master card
- 🔁 one rule per part
- 🔁 motor-age perspective
- 🧠 Full-card chant: ‘steer, circle, gate, weave, count, push, twist’.
- 🏠 Daily: every motor is NIAB sinθ at work.
- 🏠 Daily: this chapter’s puzzle birthed relativity.
Quick revision
- Eight parts on one card — force, motion, selectors, fields, laws, meters
- F = qvB sinθ · r = mv/qB · T = 2πm/qB · v = E/B
- Biot-Savart wire: μ₀I/2πr · solenoid: μ₀nI · Ampere: ∮B·dl = μ₀I
- Wire force: BIl · pair: μ₀I₁I₂/2πd · torque: NIAB sinθ
- Right-hand rules everywhere: force, grip, and circulation
- The one-rule-per-part recap
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