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Exam level1 past question

Motional EMF

Motional EMF is the voltage induced in a conductor moving through a magnetic field, depending on the speed, length, and orientation of the conductor.

Why this shows up in the exam

You may be asked to calculate the EMF generated in moving conductors or rotating coils in NEET.

How NEET tests this

Numerical · 2 QsApplicationDirect recall

Learn the idea

Motional EMF is the voltage produced when a conductor cuts magnetic lines of force; the emf equals the rate of change of magnetic flux through the circuit.

🧠 Memory hook: NABω – ‘NAB’ sounds like ‘nab’ the voltage, and the ω reminds you it’s a rotating ‘spin’

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • ε = - dΦ/dt (Faraday’s law)
  • Φ = N·B·A·cosθ for a coil of N turns
  • ε = B·ℓ·v·sinθ for a straight moving conductor
  • For a rotating coil ε = N·B·A·ω·sin(ωt)
  • Maximum emf ε₀ = N·B·A·ω
  • Resistance of the coil does not appear in the emf expression

How to approach it

  1. 1Write the magnetic flux Φ through the moving/rotating conductor
  2. 2Differentiate Φ with respect to time to get ε = -dΦ/dt
  3. 3Insert the given motion (v or ω) and geometry (ℓ, A, N)
  4. 4Take the absolute value; the peak occurs when the sine term =1
  5. 5Ignore any resistance when asked for the emf magnitude

Worked example — watch it click

In an AC generator, a coil with N turns all of the same area A and total resistance R, rotates with frequency ω in a magnetic field B. The maximum value of emf generated in the coil will be:

  • A)NABRω
  • B)NAB
  • C)NABR
  • ✅NABω

The concept behind this problem

The problem requires converting the rotating coil’s changing flux into an emf using Faraday’s law and recognizing that the coil’s resistance only affects current, not the induced emf magnitude.

Step by step

  1. 1For a coil rotating in magnetic field, flux φ=NABcosθ=NABcos(ωt).
  2. 2Induced emf e=-dφ/dt=NABωsin(ωt).
  3. 3Maximum emf e₀=NABω.
  4. 4Resistance R doesn't affect the induced emf magnitude.

Watch out

Students often mistakenly multiply the maximum emf by the coil resistance, writing NABωR instead of NABω.

Common slip-ups that cost marks

  • •Confusing angular speed ω with ordinary frequency f (ω = 2πf)
  • •Omitting the sinθ factor for a conductor not moving perpendicular to B
  • •Putting the coil resistance R into the emf formula

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 1NEET 2006

In an AC generator, a coil with N turns all of the same area A and total resistance R, rotates with frequency ω in a magnetic field B. The maximum value of emf generated in the coil will be:

Push further

More challenging

2 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 2

A U-shaped conductor is placed in a uniform magnetic field of 0.6 T directed perpendicular to its plane. A straight conducting rod of length 0.2 m is placed on the U-shaped conductor and moves with a constant velocity of 5 m/s. What is the induced EMF across the ends of the moving rod?

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