Electromagnetic Induction & Faraday’s Law
(Ideal for AP EAMCET – Physics)
1. What is Electromagnetic Induction?
- Definition: When the magnetic field passing through a loop of wire changes, a small electric voltage (EMF) appears across the loop.
- Analogy: Imagine a river (magnetic field) flowing past a paddle wheel (wire loop). If the river speed changes, the wheel starts spinning, generating energy.
- Why it matters: It’s how generators, transformers, and many appliances work.
2. Key Ideas
| Concept | Simple View |
|---|---|
| Magnetic Flux (Φ) | “How much river water passes through a paddle wheel.” It’s the product of magnetic field strength (B), the area of the loop (A), and the cosine of the angle (θ) between the field and the loop’s normal. |
| Induced EMF (ε) | “The voltage pulled by the spinning wheel.” It appears whenever Φ changes. |
| Faraday’s Law | “The change in river flow instantly creates a voltage.” |
| Lenz’s Law | “The wheel always pushes back to keep the river flow steady.” It tells the direction of the induced current. |
3. Faraday’s Law (Simple)
ε = – N dΦ/dt
- ε = induced voltage (Volts)
- N = number of turns in the coil
- dΦ/dt = how fast the magnetic flux changes (Wb/s)
- – sign = Lenz’s Law (opposes the change)
Plain English:
The voltage you feel is proportional to how quickly the magnetic field through the loop is changing, and the coil’s turns amplify it.
4. Calculating Induced EMF – Tiny Example
Scenario
A coil of 10 turns, area 0.02 m², moves straight out of a uniform magnetic field of 0.5 T at a constant speed of 0.1 m/s.
Step‑by‑Step
-
Flux change rate
- When the coil completely leaves the field, the flux goes from (Φ_{\text{inside}} = B·A = 0.5·0.02 = 0.01) Wb to 0 Wb.
- The change happens in the time it takes the coil to travel its own width (≈ 0.1 m).
- So, (dΦ/dt ≈ 0.01 \text{Wb} / 0.1 \text{s} = 0.1) Wb/s.
-
Apply Faraday’s Law
- (ε = – N·dΦ/dt = – 10·0.1 = – 1) V.
- The negative sign tells you the direction of the induced voltage; the magnitude is 1 V.
Result
A 1‑Volt voltage appears across the coil as it leaves the magnetic field.
5. How to Know the Direction (Lenz’s Law)
- Think of the change – Is the magnetic flux going up or down?
- Oppose the change – The induced current will create its own magnetic field that counteracts the change.
- Use a right‑hand rule (if you want a quick check):
- Point the thumb in the direction of the coil’s induced magnetic field.
- Your fingers show the direction of current flow in the coil.
Remember: The sign in Faraday’s law already includes this opposition.
6. Common Forms of Induction
| Situation | What Happens | Typical Equation |
|---|---|---|
| Moving coil | Flux changes because the coil moves relative to the field. | (ε = –N B A v) (when moving straight out of a field) |
| Rotating coil | Flux changes because the angle changes. | (ε = –N B A ω \sin(ωt)) |
| Changing field | The field itself varies (e |