Electromagnetic induction applications — generator, transformer, eddy currents

Question

How do generators, transformers, and eddy current devices work based on electromagnetic induction? What is the underlying principle for each?

Solution — Step by Step

A coil of $N$ turns and area $A$ rotates with angular velocity $\omega$ in a uniform magnetic field $B$ . The magnetic flux through the coil changes continuously:

\Phi = NBA\cos(\omega t)

By Faraday’s law, the induced EMF is:

\varepsilon = -\frac{d\Phi}{dt} = NBA\omega\sin(\omega t)

The peak EMF is $\varepsilon_0 = NBA\omega$ . The output is sinusoidal (AC). Slip rings and brushes transfer the current to the external circuit.

A transformer transfers electrical energy between two coils wound on the same iron core using mutual induction.

The AC in the primary coil creates a changing magnetic flux in the core, which induces an EMF in the secondary coil.

\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}

Step-up: $N_s > N_p$ (increases voltage, decreases current)
Step-down: $N_s < N_p$ (decreases voltage, increases current)

For an ideal transformer: $V_p I_p = V_s I_s$ (power is conserved).

When a conductor moves through a magnetic field (or when the field through it changes), loops of current (eddy currents) are induced within the conductor itself.

Harmful effects: Energy loss as heat in transformer cores, motors Remedy: Laminated cores (thin insulated sheets reduce eddy current loops)

Useful applications:

Electromagnetic braking (no friction wear)
Induction furnace (heat generation)
Speedometers
Metal detectors

graph TD
    A[Faraday's Law] --> B[Changing flux induces EMF]
    B --> C[AC Generator]
    B --> D[Transformer]
    B --> E[Eddy Currents]
    C --> F["Rotating coil: EMF = NBAw sin wt"]
    D --> G["Mutual induction: Vs/Vp = Ns/Np"]
    E --> H["Bulk conductor currents"]
    H --> I[Harmful: core losses]
    H --> J[Useful: braking, heating]

Why This Works

All three applications are governed by Faraday’s law of electromagnetic induction:

\varepsilon = -\frac{d\Phi_B}{dt}

The negative sign (Lenz’s law) ensures the induced current opposes the change that caused it — this is nature’s way of conserving energy.

Device	Principle	Energy Conversion
AC Generator	EMI (changing flux by rotation)	Mechanical $\to$ Electrical
Transformer	Mutual induction	Electrical $\to$ Electrical (voltage change)
Eddy current brake	EMI (conductor in changing field)	Kinetic $\to$ Heat
Induction furnace	Eddy currents	Electrical $\to$ Heat

Alternative Method

For JEE numericals on generators, remember:

Peak EMF: $\varepsilon_0 = NBA\omega$
RMS EMF: $\varepsilon_{rms} = \frac{\varepsilon_0}{\sqrt{2}}$
Frequency: $f = \omega / 2\pi =$ rotational frequency of the coil

For transformers: efficiency $= \frac{V_s I_s}{V_p I_p} \times 100\%$ . Real transformers have 90-99% efficiency. Losses come from: copper loss (resistance heating), iron loss (eddy currents + hysteresis), and flux leakage.

Common Mistake

Students write the generator EMF as $\varepsilon = NBA\omega\cos(\omega t)$ , which gives zero EMF at $t = 0$ . Whether the expression uses sin or cos depends on the initial position of the coil. If the coil starts parallel to the field (flux = 0 at $t = 0$ ), use $\cos$ for flux and $\sin$ for EMF. If the coil starts perpendicular to the field, use $\sin$ for flux and $\cos$ for EMF. Always check the initial condition given in the question.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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