Q1. A coil of 500 turns experiences a flux change from 0.1 Wb to 0.4 Wb in 0.2 s. Find the induced EMF.
dΦ = 0.4 − 0.1 = 0.3 Wb
EMF = N dΦ/dt = 500 × 0.3 / 0.2
EMF = 750 V
Electromagnetic Induction — Class 12
Move a magnet near a coil and you make electricity. Learn the laws behind every generator and transformer, and compute the induced EMF.
Magnetic flux (Φ)The amount of magnetic field passing through an area: Φ = B·A·cosθ. Unit: weber (Wb).
Faraday's lawThe induced EMF equals the negative rate of change of flux: EMF = −N·dΦ/dt. A changing flux drives a current.
Lenz's lawThe induced current always opposes the change that produced it (the minus sign) — a statement of energy conservation.
Motional EMF & inductanceA rod of length L moving at speed v across a field B generates EMF = BLv. Self-inductance stores energy U = ½LI².
Motional EMF calculator Interactive
Find the EMF induced in a rod moving perpendicular to a magnetic field (EMF = BLv).
EMF = B·L·v—V
The faster the rod moves (or the stronger the field), the larger the induced EMF — that is how a bicycle dynamo works.
Numericals practice Interactive
Motional-EMF and flux-change problems with steps.
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Solved numericals
Q2. An aircraft with a wingspan of 20 m flies at 250 m/s where the vertical component of Earth's field is 5×10⁻⁵ T. Find the EMF across the wings.
EMF = B L v
EMF = 5×10⁻⁵ × 20 × 250
EMF = 0.25 V
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Magnetic flux | Φ = B A cosθ | weber (Wb) |
| Faraday's law | EMF = −N dΦ/dt | volt (V) |
| Motional EMF | EMF = B L v | V |
| Self-induced EMF | EMF = −L dI/dt | V |
| Energy in an inductor | U = ½ L I² | J |
Common mistakes & exam wins
- Lenz's law (the minus sign) is really conservation of energy — the induced current opposes the change.
- EMF is induced only while the flux is CHANGING; a steady field gives no EMF.
- Eddy currents (induced in solid metal) are used in electromagnetic braking and induction furnaces.
- Flux Φ = BA cosθ is maximum when the area is perpendicular to the field (θ = 0°).
Frequently asked questions
What is Faraday's law of electromagnetic induction?
The magnitude of the induced EMF in a circuit equals the rate of change of magnetic flux linked with it: EMF = −N·dΦ/dt.
What is Lenz's law?
The direction of an induced current is always such that it opposes the change in flux that caused it — a consequence of conservation of energy.
What is motional EMF?
The EMF induced when a conductor of length L moves with velocity v across a magnetic field B: EMF = BLv.
What are eddy currents?
Loops of induced current set up in a solid conductor by a changing magnetic field; they cause heating and are used in braking and induction heating.