🧲 Motional Electromotive Force (EMF)

Slide a conductor through a magnetic field or spin it around—either way, the changing magnetic flux 👇 creates an emf. We call this motional emf.

1 · Straight conductor in a uniform magnetic field

  • Imagine a rectangular loop where one side (length l) can slide at speed v inside a uniform field B ⬆️.
  • The changing area changes the magnetic flux: \( \Phi_B = B\,l\,x \).
  • Differentiating gives the emf: \( \displaystyle \varepsilon = -\frac{d\Phi_B}{dt} = B\,l\,v \). :contentReference[oaicite:0]{index=0}
  • This formula is super-handy for quick NEET calculations!

2 · Lorentz-force viewpoint

  • Every charge \( q \) in the sliding rod feels the magnetic part of the Lorentz force: \( F = q\,v\,B \) (toward the rod’s far end).
  • The work done in pushing the charge from one end to the other is \( W = q\,v\,B\,l \). Divide by \( q \) and you get the same emf: \( \varepsilon = B\,l\,v \). :contentReference[oaicite:1]{index=1}

3 · Why time-varying magnetic fields create electric fields

  • If the conductor stands still (v = 0) while the magnetic field changes, the magnetic part of \( q(\mathbf{E}+\mathbf{v}\times\mathbf{B}) \) vanishes and only an induced electric field \( \mathbf{E} \) can push charges. That’s Faraday’s big idea—changing magnetism makes electricity! ⚡ :contentReference[oaicite:2]{index=2}

4 · Classic rotating-rod example

Spin a 1 m rod in a 1 T field at 50 rev s–1:

  • At radius r, speed is \( v = \omega r \) with \( \omega = 2\pi \times 50 \).
  • Add up tiny emf slices \( d\varepsilon = B\,v\,dr \) from center to rim and you get \( \displaystyle \varepsilon = \tfrac12 B\,\omega R^{2} \).
  • Plug in the numbers ➡️ \( \varepsilon = 157\;{\rm V} \). 💥 :contentReference[oaicite:3]{index=3}

5 · Spoked-wheel quick check

  • Ten 0.5 m spokes spin at 120 rev min–1 in Earth’s horizontal field \( H_E = 0.4\;{\rm G} = 0.4 \times 10^{-4}\;{\rm T} \).
  • Use the same rotating-rod formula: \( \displaystyle \varepsilon = \tfrac12 B\,\omega R^{2} = 6.28 \times 10^{-5}\;{\rm V} \). :contentReference[oaicite:4]{index=4}
  • The number of spokes doesn’t matter because the spokes are in parallel.

🎯 High-Yield Ideas for NEET

  1. Formula focus: \( \varepsilon = B\,l\,v \) for a straight, sliding rod. Quick plug-and-play! :contentReference[oaicite:5]{index=5}
  2. Rotational trick: For any radius-R rotor, \( \varepsilon = \tfrac12 B\,\omega R^{2} \). :contentReference[oaicite:6]{index=6}
  3. Direction rule: Use Lorentz force \( q(\mathbf{v}\times\mathbf{B}) \) to spot charge flow and hence current direction. :contentReference[oaicite:7]{index=7}
  4. No flux change ⇒ no emf: A static magnetic flux (or just changing electric flux) won’t light the bulb. :contentReference[oaicite:8]{index=8}
  5. Changing B creates E: Even a resting conductor feels an induced electric field when \( B \) varies with time. :contentReference[oaicite:9]{index=9}

Keep practicing with different speeds, lengths, and fields. You’ve got this! 😊