JEE/NEET Physics · Electromagnetic Induction series · Part 3 of 6 · All parts →
- Rod of length ℓ moving at v ⊥ to B: EMF ε = Bℓv across its ends
- Origin: magnetic force pushing the rod’s charges to the ends — a charge pump
- In a closed rail circuit: current I = Bℓv/R, and a retarding force F = B²ℓ²v/R
- Power dissipated = mechanical power supplied: BIℓv — the books balance
- Rotating rod: ε = ½Bωℓ² (the area-sweeping view)
Slide a metal rod along rails in a magnetic field and it becomes a battery — the magnetic force piles up charges at its ends. This ‘motional EMF’ is Faraday’s law you can hold in your hand, and the seed of every generator. Part 3 of the Electromagnetic Induction series.
- The charge pump
- The rail circuit
- The retarding force and power balance
- The rotating rod
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
The Charge Pump
Rod moving at v in field B: each free charge inside also moves at v, feeling F = qvB sideways along the rod. Charges pile at one end, vacate the other — an EMF appears across the rod:
The Rail Circuit
Let the rod slide on connected rails through resistance R: current flows, I = Bℓv/R. But now the current-carrying rod feels the motor force F = BIl opposing its motion — to keep sliding, you must pull with that force. Nothing is free.
The Retarding Force and Power Balance
The Rotating Rod
Spin a rod of length ℓ about one end at ω in field B: it sweeps area per second ½ℓ²ω, giving ε = ½Bωℓ² — Faraday’s area-change route in rotational form.
Solved Examples
ε = 0.2 × 0.5 × 4 = 0.4 V.
✔
Answer: 0.4 V
I = 0.4/2 = 0.2 A; F = 0.2×0.2×0.5… F = BIl = 0.2×0.2×0.5 = 0.02 N; P = Fv = 0.08 W = I²R ✔.
✔
Answer: 0.2 A; 0.02 N; 0.08 W
ε = ½Bωℓ² = ½ × 0.5 × 10 × 1 = 2.5 V.
✔
Answer: 2.5 V
- Angles forgotten. ε = Bℓv needs ℓ ⊥ B ⊥ v: any misalignment brings a sin factor.
- Force direction on the rod. The retarding force opposes MOTION (Lenz again): it never aids the slide.
- Skipping the power check. Fv must equal I²R: if not, a sign or formula slipped — always audit.
- Using full ℓ² for the rotating rod. It’s ½Bωℓ²: the swept-area rate already carries the half.
This Physics in Your Daily Life
- Faraday’s original experiments — sliding contacts and moving coils: this exact geometry birthed the electrical age.
- Bicycle dynamos — a spinning magnet near the wheel induces in a coil (the rotating-rod idea’s cousin): your light powered by your legs.
- Space tethers — km-long wires orbiting through Earth’s field generate motional EMF: tested by NASA as orbit power.
- Electric guitars’ pickups (inverse) — moving steel strings changing flux in fixed coils: rock music via relative motion, rod-style.
- Induction hardening and rail-braking — relative motion of conductor and field engineered for heat or drag: industry full of Bℓv.
A river pushes a waterwheel: the moving water’s momentum becomes rotation. A field ‘pushes’ a rod’s charges: their drift becomes piled-up ends — voltage. The rod is a pump with no moving parts except itself: motion through field is the entire engine.
1 m rod at 5 m/s in 0.1 T: 0.5 V. At 50 m/s: 5 V — linear in speed, which is why generator RPM and voltage scale together, and why your dynamo’s brightness follows pedalling speed.
Side-view the rod: charges drawn drifting to one end, leaving the other depleted; the internal field E that builds between the ends fights further piling until equilibrium E = vB. That internal balance IS the EMF — the picture derives Bℓv in three strokes.
Practice set (answers hidden — try first)
(NEET-level) ℓ=0.2, v=10, B=0.5 (⊥): ε =
(JEE Main-level) Rod on R=1 Ω rails, ε=2 V: I and F at ℓ=1, B=0.5:
(NEET-level) Doubling v: ε
(Concept) The retarding force on a sliding rod exists because
(JEE Main-level) Rod ω=20 rad/s, ℓ=0.5 m, B=0.4: ε =
- ε = Bℓv (perpendicular trio)
- rails: I = Bℓv/R
- retarding F = B²ℓ²v/R (Lenz)
- power balance: Fv = I²R
- rotating rod: ½Bωℓ²
- 🔁 motional EMF formula
- 🔁 rail circuit mechanics
- 🔁 retarding-force origin
- 🧠 Chant: ‘B-ℓ-v, all perpendicular’.
- 🧠 Audit: ‘your pull power = the resistor’s heat’.
- 🏠 Daily: bicycle dynamos glow with pedalling speed.
- 🏠 Daily: space tethers orbit-generate by Bℓv.
Quick revision
- Rod of length ℓ moving at v ⊥ to B: EMF ε = Bℓv across its ends
- Origin: magnetic force pushing the rod’s charges to the ends — a charge pump
- In a closed rail circuit: current I = Bℓv/R, and a retarding force F = B²ℓ²v/R
- Power dissipated = mechanical power supplied: BIℓv — the books balance
- Rotating rod: ε = ½Bωℓ² (the area-sweeping view)
- The retarding force and power balance
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