Given below are two statements:
Statement I: For a closely wound coil of N turns, with the same change of flux through each turn, the induced emf is N times the emf induced in a single turn.
Statement II: When a coil is rotated in a steady, uniform magnetic field about an axis parallel to the field, an emf is induced in it.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Statement I is correct but Statement II is incorrect.
By Faraday’s law, an emf is induced whenever the magnetic flux \( \Phi_B=BA\cos\theta \) through a circuit changes. Its magnitude equals the rate of change of this flux.
Statement I For a closely wound coil of N turns, with the same change of flux through each turn, the induced emf is N times the emf induced in a single turn. — True. Each turn has the same emf \( d\Phi_B/dt \). The turns are in series, so their emfs add to give \( \varepsilon=-N\,d\Phi_B/dt \).
Statement II When a coil is rotated in a steady, uniform magnetic field about an axis parallel to the field, an emf is induced in it. — False. In a steady field the flux can change only through the angle \( \theta \) between \( \vec{B} \) and the area vector. When the axis of rotation is parallel to \( \vec{B} \), the area vector turns around the direction of the field. It keeps the same angle with the field, so the flux stays constant and no emf is induced. An ac generator gives an emf because its coil turns about an axis perpendicular to the field.
NCERT (2026-27):
Faraday’s Law of Induction – “In the case of a closely wound coil of N turns, change of flux associated with each turn, is the same. Therefore, the expression for the total induced emf is given by”
\( \displaystyle \varepsilon=-N\frac{d\Phi_B}{dt} \)\( \qquad (6.4) \)
Faraday’s Law of Induction – “… The flux can also be altered by changing the shape of a coil (that is, by shrinking it or stretching it) in a magnetic field, or rotating a coil in a magnetic field such that the angle θ between B and A changes. In these cases too, an emf is induced in the respective coils.”