Electromagnetic Induction

Electromagnetic InductionNEET Physics · Class 12 · NCERT Chapter 6

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7 interactive concept widgets for Electromagnetic Induction. Drag any slider, change any number, and watch the formula and the answer update live. Built so you understand how each NEET problem actually works, not just the final number.

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Magnetic flux through a coil

Faraday induced EMF

Lenz's law direction

Motional EMF in a sliding rod

Self-inductance of a solenoid

Mutual inductance

Energy stored in an inductor

Flux and Faraday

Magnetic flux and the law that connects its rate of change to induced EMF.

Flux

Magnetic flux through a coil

Φ = B A cos θ. The starting point for Faraday's law.

Magnetic flux through a flat area: Phi = B A cos theta. Maximum when normal is parallel to B; zero when perpendicular.

B: 0.50 T

Area A: 100 cm²

θ between normal and B: 30°

Magnetic flux Φ

4.330e-3 Wb

Φ = B \cdot A = B A cos θ

Try this

θ = 0°: maximum flux. Loop face perpendicular to B.
θ = 90°: zero flux. Loop edge-on to B.
Flux is the basis of Faraday's law: only its CHANGE produces EMF.
1 Wb = 1 T·m². Big units; lab values are usually mWb or µWb.

Faraday

Faraday's law of induction

Induced EMF = -N dΦ/dt.

Induced EMF in a coil of N turns when flux changes by ΔΦ over time Δt.

Turns N: 50

ΔΦ: 5.00 mWb

Δt: 100 ms

Induced EMF

2.500 V

ϵ = - N \frac{ΔΦ}{Δ t}

Try this

Faster flux change (smaller Δt) gives bigger EMF.
More turns multiply EMF.
Sign comes from Lenz's law: induced current opposes the change.

Lenz

Lenz's law direction

Induced current always opposes the change in flux that creates it.

A bar magnet moves near a closed coil. Lenz's law says the induced current opposes the change in flux.

Flux change: increasing (into the loop, say from top)

Induced field direction: OPPOSITE to B (so out of the top)

Coil acts as: N pole faces the magnet (to repel)

ϵ = - \frac{d Φ}{d t}

Try this

Magnet approaching → repulsive force (work must be done against the induced field). This is where the energy comes from.
Magnet receding → attractive force (still work done, in the receding direction).
Lenz's law is energy conservation in disguise.

Motional EMF and inductance

A sliding rod, a self-inductor, and a transformer-style mutual inductor.

Motional EMF

Motional EMF in a sliding rod

A rod sliding on rails through B generates EMF = B L v.

A conducting rod of length L slides on rails with velocity v in a perpendicular field B. EMF = B L v.

B: 0.50 T

L: 0.50 m

v: 2.00 m/s

Circuit R: 0.50 Ω

EMF

0.500 V

ϵ = B Lv

1.000 A

Drag F

0.250 N

Power P

0.500 W

Try this

You must keep pushing the rod with force F = B I L to overcome the induced drag.
Power input by you = power dissipated in R: F v = I² R.
No source of EMF in the circuit; the rod is the EMF source.

Self-induction

Self-inductance of a solenoid

L = mu_0 N² A / l. Back EMF = L di/dt.

Self-inductance of a long solenoid with N turns, area A and length l. The faster the current changes, the bigger the back EMF.

Turns N: 500

Area A: 10.0 cm²

Length l: 20.0 cm

di/dt: 2 A/s

Self-inductance L

1.571 mH

L = \frac{μ _{0} N ^{2} A}{l}

Back EMF

0.003 V

∣ ϵ ∣ = L d i / d t

Try this

Doubling N quadruples L (N² scaling).
Filling the solenoid with iron (high mu_r) multiplies L by mu_r.
Current cannot change instantly through an inductor: di/dt would be infinite.

Mutual induction

Mutual inductance

The coupling that makes transformers work.

Two coils linked by flux: changing current in one induces an EMF in the other. Mutual inductance M is the coupling constant.

N₁ (primary): 500

N₂ (secondary): 200

Common A: 10.0 cm²

Length l: 20 cm

di₁/dt: 2 A/s

Mutual inductance M

0.628 mH

M = \frac{μ _{0} N _{1} N _{2} A}{l}

Induced EMF in secondary

0.001 V

∣ ϵ_{2} ∣ = M d i_{1} / d t

Try this

M depends only on geometry; same M whether you drive coil 1 or coil 2.
Transformer is two coils with high M, sharing an iron core.
k = M/sqrt(L_1 L_2) is the coupling coefficient. k = 1 for perfect coupling.

Energy in an inductor

How much energy lives in the magnetic field of an inductor.

Energy

Energy stored in an inductor

U = ½ L I². Stored in the magnetic field.

An inductor stores energy in its magnetic field. Same form as the kinetic energy formula (½ m v²).

Inductance L: 50.0 mH

Current I: 2.00 A

Stored energy

100.000 mJ

U = \frac{1}{2} L I^{2}

Try this

Doubling I quadruples U.
When you turn off a circuit with a big inductor, the stored energy can produce a spark across the switch.
Energy density in the field: u = B² / (2 μ₀).

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