“Nature hates the change”
Lenz's law
The induced current always opposes the change that caused it. Push a magnet in and it pushes back; pull it out and it pulls after you. This is conservation of energy wearing a minus sign.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Electromagnetic Induction formulas
Induction is one sentence with many consequences: a changing magnetic flux makes an EMF, and the minus sign in Lenz's law is where the physics lives. Almost every question here is a test of whether you can say what the induced current is opposing.
14 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
Flux and Faraday's law
| What | Formula | Symbols and notes |
|---|---|---|
| Magnetic flux | Φ = BA cosθ | unit weber; θ is measured from the normal to the area |
| Faraday's law | e = −dΦ/dt | for N turns, e = −N dΦ/dt |
| Motional EMF | e = Blv | a rod of length l moving with speed v across a field |
| Induced current | I = e/R | and the charge that flows is q = ΔΦ/R |
| Rotating coil | e = NABω sin(ωt) | the basis of the AC generator |
Inductance
| What | Formula | Symbols and notes |
|---|---|---|
| Self inductance | e = −L dI/dt | L is in henry |
| Inductance of a solenoid | L = μ₀n²Al | n is turns per unit length |
| Energy stored in an inductor | U = ½LI² | compare with ½CV² for a capacitor |
| Mutual inductance | e₂ = −M dI₁/dt | M depends on the geometry and the coupling |
| Coils in series | L = L₁ + L₂ ± 2M | plus when the fluxes help each other |
Eddy currents and transformers
| What | Formula | Symbols and notes |
|---|---|---|
| Transformer ratio | Vs/Vp = Ns/Np = Ip/Is | step-up means more turns on the secondary and less current |
| Ideal transformer | VpIp = VsIs | power in equals power out |
| Efficiency | η = output power/input power | losses are copper, iron, hysteresis and flux leakage |
| Eddy currents | circulating currents in a solid core | reduced by laminating the core |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Transformers change voltage, never power”
Step-up and step-down
More turns means more volts and less current. An ideal transformer gives out exactly what it takes in, so nothing is gained for free.
“Transformers refuse DC”
Why a transformer needs AC
Steady current gives constant flux, so dΦ/dt is zero and no EMF is induced. Only a changing current works.
Where marks go
The mistakes that cost the most.
- Dropping the minus sign in Faraday's law. It is Lenz's law and it is usually worth a mark on its own.
- Thinking an EMF needs a strong field. It needs a changing flux; a strong steady field induces nothing.
- Confusing flux with field. Flux includes the area and the angle.
- Expecting a transformer to work on DC.
- Forgetting that the induced charge q = ΔΦ/R depends on the total change in flux, not on how fast it changed.
Test yourself
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