Faraday’s Law of Induction ⚡

1. Magnetic Flux 🌟

  • You find magnetic flux through a flat area with
    \( \Phi_B = B A \cos \theta \) — here B is field strength, A is area, and θ is the angle between B and the area’s normal. :contentReference[oaicite:0]{index=0}
  • For curved or non-uniform surfaces, add up the tiny pieces:
    \( \displaystyle \Phi_B = \sum_i B_i\,\Delta A_i \). :contentReference[oaicite:1]{index=1}
  • Unit: 1 weber (Wb) = 1 tesla·m².

2. What Faraday Saw 🔍

Move a magnet toward or away from a coil, or move a current-carrying coil near another coil, and the magnetic flux through the test coil changes. That change sets up an emf, so current flows and the galvanometer jumps. When the flux stops changing, the current stops too. :contentReference[oaicite:2]{index=2}

3. Faraday’s Law 🚀

“The induced emf equals the rate at which magnetic flux changes.”
\( \displaystyle \varepsilon = -\frac{d\Phi_B}{dt} \)   (minus sign points to current direction, see Lenz’s idea next section). :contentReference[oaicite:3]{index=3}

For a coil with N tightly packed turns:
\( \displaystyle \varepsilon = -N\frac{d\Phi_B}{dt} \) :contentReference[oaicite:4]{index=4}

4. How to Boost the Induced emf 💡

  • Add more turns (N) — emf grows in direct proportion. :contentReference[oaicite:5]{index=5}
  • Change B, A, or θ faster. Shrink/stretch the coil or spin it so θ swings. :contentReference[oaicite:6]{index=6}
  • Practical trick set (Example 6.1): slide a soft-iron core inside the driving coil, use a stronger battery, and move everything quickly toward the test coil. :contentReference[oaicite:7]{index=7}
  • No galvanometer handy? Replace it with a tiny torch bulb; the bulb glows when current flows. :contentReference[oaicite:8]{index=8}

5. Worked-Out Examples 🧮

Example A — Shrinking Field in a Square Loop

Square loop: side = 10 cm, R = 0.5 Ω. Field 0.10 T points north-east, then drops to 0 T in 0.70 s.
Induced \( \varepsilon = 1.0\;{\rm mV} \), current \( I = 2\;{\rm mA} \). :contentReference[oaicite:9]{index=9}

Example B — Flipping a Coil in Earth’s Field

Circular coil: radius = 10 cm, N = 500, R = 2 Ω. Rotate it 180° in 0.25 s in the horizontal component of Earth’s field (3 × 10-5 T).
Induced \( \varepsilon \approx 3.8\;{\rm mV} \), current \( I \approx 1.9\;{\rm mA} \). :contentReference[oaicite:10]{index=10}

6. Quick NEET Checklist ✅

  1. \( \Phi_B = B A \cos \theta \) — base formula for flux.
  2. \( \varepsilon = -\dfrac{d\Phi_B}{dt} \) — heart of Faraday’s law.
  3. For N turns, multiply emf by N.
  4. Faster change in B, A or θ means bigger emf.
  5. Direction clue sits in the minus sign (ties directly to Lenz’s law in the next sub-topic).

Keep experimenting — Michael Faraday did, and look where it led! 🤓