Identify the correct statements among the following:
A. The emf induced in a coil is directly related to the rate of change of magnetic flux through it.
B. Inductance of a coil is the ratio of the flux-linkage to current.
C. The magnetic flux passing through a coil is maximum, when the plane of the coil is perpendicular to the magnetic field.
D. Inductance of a coil is the ratio of the rate of change of current through it and magnetic flux linked to it.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A, B and C only
(A) The emf induced in a coil is directly related to the rate of change of magnetic flux through it. — Correct. This is Faraday’s law, \( \varepsilon = -d\Phi/dt \).
(B) Inductance of a coil is the ratio of the flux-linkage to current. — Correct. The self-inductance is defined by \( N\Phi = LI \), i.e. \( L = N\Phi/I \).
(C) The magnetic flux passing through a coil is maximum, when the plane of the coil is perpendicular to the magnetic field. — Correct. \( \Phi = BA\cos\theta \), where \( \theta \) is the angle between \( \vec{B} \) and the normal to the plane. When the plane is perpendicular to \( \vec{B} \), the normal is along \( \vec{B} \), \( \theta = 0 \) and \( \Phi = BA \), the maximum.
(D) Inductance of a coil is the ratio of the rate of change of current through it and magnetic flux linked to it. — Incorrect. Inductance is flux linkage per unit current, or equivalently the induced emf per unit rate of change of current, \( |\varepsilon| = L\,dI/dt \). The ratio \( (dI/dt)/\Phi \) is not even dimensionally an inductance.
NCERT (2026-27):
Summary – “1. The magnetic flux through a surface of area A placed in a uniform magnetic field B is defined as,
\( \displaystyle \Phi_B = \mathbf{B}\cdot\mathbf{A} = BA\cos\theta \)
where \( \theta \) is the angle between B and A.
2. Faraday’s laws of induction imply that the emf induced in a coil of N turns is directly related to the rate of change of flux through it,
\( \displaystyle \varepsilon = -N\frac{d\Phi_B}{dt} \)”
Self-Inductance – “… In this case, flux linkage through a coil of N turns is proportional to the current through the coil and is expressed as
\( \displaystyle N\Phi_B \propto I, \qquad N\Phi_B = L\,I \qquad (6.13) \)
where constant of proportionality L is called self-inductance of the coil.”