An emf is produced in a coil, which is not connected to an external voltage source. This can be due to (a) the coil being in a time varying magnetic field. (b) the coil moving in a time varying magnetic field. (c) the coil moving in a constant magnetic field. (d) the coil is stationary in external spatially varying magnetic field, which does not change with time.

An emf is produced in a coil, which is not connected to an external voltage source. This can be due to (a) the

NCERT Exemplar · Q29

Q. An emf is produced in a coil, which is not connected to an external voltage source. This can be due to

(a) the coil being in a time varying magnetic field.

(b) the coil moving in a time varying magnetic field.

(d) the coil is stationary in external spatially varying magnetic field, which does not change with time.

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Concept understanding — Electromagnetic Induction

Electromagnetic Induction

Electromagnetic induction is the phenomenon in which a changing magnetic flux through a circuit produces an electromotive force (emf) — and hence a current, if the circuit is closed. It is the single idea behind generators, transformers, inductors, and the entire AC power grid.

The Central Discovery

Michael Faraday found (1831) that a current is induced in a coil not when a magnet sits still near it, but only while the magnet moves — that is, only while the magnetic flux linked with the coil is changing. A steady magnet, however strong, induces nothing.

Magnetic Flux

The key quantity is magnetic flux $\Phi_B$ through a surface of area $A$ in a field $\vec{B}$ :

\Phi_B = \vec{B} \cdot \vec{A} = BA\cos\theta

where $\theta$ is the angle between $\vec{B}$ and the area's normal. Its SI unit is the weber (Wb), where $1\ \text{Wb} = 1\ \text{T}\cdot\text{m}^2$ .

Flux can change in three distinct ways, and any of them induces an emf:

the field strength $B$ changes,
the area $A$ of the loop changes,
the orientation $\theta$ changes (a coil rotating in a field — the basis of the generator).

Faraday's Law

The induced emf equals the negative rate of change of flux. For a coil of $N$ turns:

\mathcal{E} = -N\,\frac{d\Phi_B}{dt}

The faster the flux changes, the larger the emf. This is why a magnet dropped quickly through a coil gives a bigger deflection than one moved slowly.

Lenz's Law — the Minus Sign

The negative sign expresses Lenz's law: the induced current flows in the direction that opposes the change producing it. Push a magnet's north pole toward a coil, and the coil's near face becomes a north pole to repel it; pull it away, and the face becomes a south pole to attract it. This is simply energy conservation — you must do work against this opposition, and that work becomes the electrical energy of the induced current.

Motional emf

A special, very useful case: a conducting rod of length $l$ moving with speed $v$ perpendicular to a field $B$ sweeps out area and develops an emf

\mathcal{E} = Blv

Here the emf arises because the free charges in the rod experience a magnetic force $q\vec{v}\times\vec{B}$ , which drives them along the rod. …

Why this formula?

Electromagnetic Induction

Electromagnetic induction is the effect discovered by Faraday: a changing magnetic flux through a circuit drives an induced EMF (and hence a current). The key word is changing — a steady field, however strong, induces nothing.

Magnetic flux

Flux measures how many field lines thread a surface bounded by the loop:

\Phi_B = \int \vec{B} \cdot d\vec{A} = BA\cos\theta

It can change three ways: by changing $B$ , by changing the area $A$ , or by rotating the loop (changing $\theta$ ).

Faraday's law

The induced EMF equals the rate of change of flux:

\mathcal{E} = -\frac{d\Phi_B}{dt}

For a coil of $N$ turns, $\mathcal{E} = -N\,\dfrac{d\Phi_B}{dt}$ . The EMF depends on how fast the flux changes, not on the flux itself — a slow change gives a small EMF, a rapid change a large one.

Lenz's law — the minus sign …

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An emf appears in a source-free coil only when the magnetic flux through it changes with time (Faraday's law). Options (a), (b) and (c) can all produce a changing flux; option (d) cannot. Correct options: (a), (b), (c).

Concept understanding. Faraday's law: $\displaystyle \mathcal{E} = -\frac{d\Phi_B}{dt}$ , with $\Phi_B = \int \vec{B}\cdot d\vec{A}$ . The flux can change because $\vec{B}$ changes with time, because the coil moves so it links a different field, or because its area/orientation changes. A field that is merely non-uniform in space but constant in time, linked by a stationary coil, gives a constant flux and hence no emf.

Testing each option.

(a) Coil in a time-varying magnetic field: $\partial\vec{B}/\partial t \neq 0$ changes the flux even with the coil at rest. Emf induced. Correct.
(b) Coil moving in a time-varying field: both the field's time variation and the motion change the flux. Emf induced. Correct. …

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Q.An emf is produced in a coil, which is not connected to an external voltage source. This can be due to

Concept understanding — Electromagnetic Induction

Electromagnetic Induction

The Central Discovery

Magnetic Flux

Faraday's Law

Lenz's Law — the Minus Sign

Motional emf

Why this formula?

Electromagnetic Induction

Magnetic flux

Faraday's law

Lenz's law — the minus sign …

Method: Testing Each Scenario Against "Is the Flux Changing With Time?"

Steps

Q.An emf is produced in a coil, which is not connected to an external voltage source. This can be due to

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